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About Abe Mantell
(Top Expert on this page)

Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience
Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

   

You are here:  Experts > Science > Math for Kids > Word Problems

Questions Answered By Expert  Abe Mantell 
In Category  Word Problems

SubjectDate Asked

Matrix Word Problem8/12/2009
  Q: I'm trying to convert the following problem into a Matrix to solve by calculator (the solving part ...
  A: Let x=# of courtside seats sold, let y=# of endzone seats sold, and let z=# of balcony seats sold. ...
Can you please show me the steps to these problems!7/23/2009
  Q: 1. Simplify : root:3:(81a^6b^8) 2. Simplify : (sqrt(100m^5n)/(sqrt(5m^3)) 3. Find the height, to ...
  A: 1. I gather you mean the cube-root, yes? cube_root(81a^6b^8), factor out perfect cubes... . ...
Word Problem...... PLease Help7/21/2009
  Q: The Gateway Arch in St.Louis is 640 ft high. How long would it take an object to fall freely from ...
  A: 1. Using s(t)=(1/2)gt^2, with s(t)=640 ft and g=32 ft/sec^2, we get . 640=16t^2 ==> t^2=40 ==> ...
Set Theory - Venn Diagram Problem7/18/2009
  Q: In a survey of 200 people, 15% don’t have driving licence, 10% were charged for parking ticket one ...
  A: Are you certain you have the problem correct? Only 15% (or 30 ppl) DO NOT have a driver's license, ...
Mathematics - Logic7/17/2009
  Q: A rectangular solid is made up of 12 cubes of the same size. The exposed surface is then painted ...
  A: It depends how the cubes are oriented. For example, if the 12 cubes are arranged to be 1 layer in ...
motion problem!7/16/2009
  Q: pls,.. i really need the answer in this problem.. kindly show the solutions.. What is the speed of ...
  A: Let b=speed of boat in still water, s=speed of the stream. Speed of boat with current is b+s, speed ...
Investment Accounts7/15/2009
  Q: An investor wants to invest $1000.00 into four amounts or accounts. He invests $1.00 in each account ...
  A: Let x=the additional amount he will invest the 2% account, y=additional amount invested in the 5% ...
Buisness math7/14/2009
  Q: Alan, I really need some help i don't understand this question. Jill Co. sells thermometers ($2) and ...
  A: Who is Mr Alan? :-o Anyhow... Let x=# of thermometers sold, y=# of water bottles sold. Thus, we ...
GMAT word problems7/10/2009
  Q: /Ms. Mantell, These are all the problems from the GMAT practices which i need you to help me. 1. An ...
  A: I am a "Mr") :-) 1. $d at k% gives $600 interest in 2 years, so $d at k% for 1 year .. will give ...
Problems involving two variables7/5/2009
  Q: I am having a very hard time understanding how to do this problem and I was wondering if you could ...
  A: Let x=# of burgers you need to buy, and y=# of hot dogs you need to buy Thus, 1. x+y=23 (since there ...
quadratic word problem6/11/2009
  Q: I'm trying to help some students with quadratic application probs. The one that I'm not sure how to ...
  A: Assuming the bucket is at ground level, with y=0, we just need to determine the x-value of where it ...
Can Help me solve this question6/9/2009
  Q: (Quadratic Equation) 1)Solve these equation.(use 2^x=y) 2^2x-9(2^x)+20=0 2)if p and q are the root ...
  A: Wow, you sure have many questions! How about I do a couple and see if you can do the others? 1. Do ...
Quadratic Function6/8/2009
  Q: Find two numbers whose sum is 30,such that the sum of their squares is a maximum.
  A: Let x=one of the numbers, then 30-x is the other. The sum of the squares will then be: x^2 + ...
Quadratic Equation6/7/2009
  Q: A strip of wire of length 28cm is cut into two pieces.One piece is bent to form a square of side x ...
  A: If the square has sides of length x, then the total perimeter is 4x. Thus, 28-4x is left over for ...
college algebra6/6/2009
  Q: Flying with the wind, a small plane can fly 600 mi in 3 h. Against the wind, the plane can fly the ...
  A: Let x=the rate of the plane in calm air, and y=the rate of the wind So, using distance=rate*time we ...
Need help with problem setup6/4/2009
  Q: I am helping a friend with her math for an upcoming test for adult education. It has been years ...
  A: 20% of the 25 ounce solution is pure alcohol, thus only 5 ounces are pure alcohol (i.e. 20% of 25 ...
Math6/3/2009
  Q: I have a question. If the question says that they give you a surface area and radius, and your ...
  A: I need to know what is the shape of the object? Is it a sphere? A cylinder? As for the vase, I ...
Systems of Equations1/13/2009
  Q: A parking lot holds 450 cars. The ratio of full size cars to compact cars is 11 : 4. How many full ...
  A: Let x=the # of full size cars, then 450-x=the # of compact cars (since the total is 450) But they ...
linear equations with 2 ordered pairs1/11/2009
  Q: To lose weight, John ate less calories each week. By the 4th week he was eating 2700 calories per ...
  A: Assuming the rate is constant (i.e. a linear relationship between caloric intake and days)...we have ...
Math1/8/2009
  Q: A man can construct a wall in 20hrs. With the help of his apprentice assistant the task would take ...
  A: The first man works at a rate of 1 wall in 20 hrs, or 1/20 of a wall/hr. Let x=the rate of the ...
math1/7/2009
  Q: When Lee gets his paycheck he pays his $550 rent his $245 car payment and his $160 student loan ...
  A: Let x=the amount of his paycheck He pays $550 + $245 + $160 = $955, thus... x-955 is what he has ...
System of Inequalities Word Problem1/5/2009
  Q: I'm currently doing final review for Algebra II and would like some help with this word problem: ...
  A: You will have one inequality for each constraint, i.e. one for the limitation of 85 hrs/day for ...
intergers1/4/2009
  Q: ummm. yeah like i dont get this "-2 times 3 times -6=?"
  A: Do you mean you want to know why -2 times 3 is -6?? Well, I hope you agree that 2 times 3 is 6, ...
math1/3/2009
  Q: 13. If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if ...
  A: The north bound plane traveled 150x2 = 300 miles (north) The west bound plane traveled 200x2 - 400 ...
equations question12/31/2008
  Q: my question says. write out in words, what each of the following equations says mathematically. (a) ...
  A: (a) The product of "a" and "b" (i.e "a" times "b") equals --- the product of "c" and "d" (i.e. "c" ...
probability-math12/26/2008
  Q: IF a teacher has prepared a 5-item test with the first three itmes being true and the last two ...
  A: I gather you meant "... the first three being TRUE/FALSE QUESTIONS ..." Yes??? If so, then: Each of ...
Math Problem help9/2/2008
  Q: For the age of 15 to 24 , motor vehicle accidents account for 31/24 of all accidental deaths, and ...
  A: I am a bit confused by the first fraction, 31/24, since it is greater than one! So, either it is ...
Word Problems for the Unknown9/1/2008
  Q: In 1955 only 435 Kaiser-Darrins were built, because Kaiser-Frazer bailed out of the car business. ...
  A: Let x=the value of the car in very nice condition. Since 1 3/4 = 7/4, we get: (7/4)x=$62,125...now ...
word problem8/31/2008
  Q: there are 7 girls on a bus, each girl has 7 back packs and in each pack pack there are 7 cats how ...
  A: There are 7x7 backpacks = 49 backpacks...there are 49x7 cats = 343 cats ...there are 343x4 cat legs ...
find the ratio of speed7/23/2008
  Q: On a straight road, an inspecting officer traveled from the rear to the front of an army column, and ...
  A: If I correctly interpret....you are saying that in the time it took the soldiers to travel their own ...
Half life7/22/2008
  Q: Polonium-210 has a half life of 138.4 days. A 268mg sample decays for 2 years(730 days). What amount ...
  A: Let A(t)=the amount of Polonium-210 remaining after t days. Then A(t)=Ao*e^(kt)...since the 1/2-life ...
answer7/21/2008
  Q: Mohan sold a watch to Tarun at 12% gain and Tarun had to sell it to manish at a loss of 5%. If ...
  A: 2/5 should sell for 2/5 of 96000 = 38400, but he sold it a 6% loss. 6% of 38400 is 2304. So, he ...
answer7/20/2008
  Q: Mohan sold a watch to Tarun at 12% gain and Tarun had to sell it to manish at a loss of 5%. If ...
  A: Let x=the price paid for the watch by Mohan. So, Mohan sold it to Tarun for x + 12% of x = x + 0.12x ...
Word problems/ Algebra7/16/2008
  Q: I am having difficulty creating the formula to solve word problems. For example:A traveling club ...
  A: Let x=the number of people initially in the club. Thus, the initial cost per person is $150,000/x, ...
Math Word Problem finding current7/15/2008
  Q: A motoboat heads upstream a distance of 12 miles on a river whose current is running at 5 miles per ...
  A: Let x=the speed of the boat relative to the water. Thus, the actual speed upstream is x-5 miles/hr, ...
math7/12/2008
  Q: melinda has 3pairs of red socks,2 pairs of black socks and 5 pairs of white socks . how many minimum ...
  A: Are you sure you mean what is the "minimum" # that can be removed? Also, I gather she needs to be ...
how do i covert in the metric system7/11/2008
  Q: I'm having a test monday and I'm having trouble converting.
  A: The easiest way to do any conversions is to use what are called "unit fractions." That is, you ...
Help Solve7/7/2008
  Q: 1.If you earned an average of $25,000 over your working life you retire after 2005 at 62, 63, or 64, ...
  A: OOPS! Sorry, disregard my previous reply to this! OK... 1. Let x=age, y=SS benefit. Thus, ...
Help Solve7/6/2008
  Q: After 2 minutes on a treadmill, Jenny has a heart rate of 82. After 3 minutes she has a heart rate ...
  A: Let x=the time (in minutes), y=heart rate. Thus, we get the two ordered pairs: (2,82) & (3,86) ...
please tell me how to do it as soon as possible7/5/2008
  Q: A salesman drove to portland a distance of 300 miles. during the last 80 miles of his trip heavy ...
  A: Let x=the original speed (in miles/hr), thus x-15=the speed during the last 80 miles. Let t=the time ...
problem solving7/2/2008
  Q: The midpoints of the sides of a square of side 1 inch are joined to form a new square. This ...
  A: Clearly, the area of the first square is 1^1 ==> A1=1 The second square has sides sqrt(2)/2, so its ...
sine and cosine word problem5/23/2008
  Q: Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 22mph in a ...
  A: After 5 hrs, the distance they have traveled is: The 22 MPH boat: 110 miles The 29 MPH boat: 145 ...
Word Problems1/22/2008
  Q: Chicken Little was going to town to sell her eggs when she bubmped into Henny Penny, who wanted to ...
  A: Let x=the number of eggs originally had. 1. she sold (1/2)x+(1/2) to Henny Penny, leaving -- ...
Cows1/18/2008
  Q: In a group of cows and turkeys; the number of heads are 35 less than the number of legs what is the ...
  A: Let c=the # of cows, and t=the # of turkeys Thus, the total number of heads is given by c+t, and ...
Sixth grade math problem1/17/2008
  Q: My son has a "Problem of the Week" that has the whole family stumped. The school newspaper is ...
  A: This is a standard problem in using Venn Diagrams. To get a little primer, check: ...
Alegebra 21/16/2008
  Q: One electronic reader can read a deck of punched cards in 1/2 the time of another reader. Together ...
  A: Let x=the rate at which the slower machine can read a deck Then x/2=the rate of the faster machine ...
Quiz Word problem1/15/2008
  Q: Steve can write a quiz in 40 minutes. Steve and Ruth working together can write a quiz in 25 ...
  A: ), Since work=rateXtime, Let r = the rate at which Ruth can work (alone) Steve can work at the ...
maths using qadratic equation1/13/2008
  Q: some students went for the picnic total cost for the food was Rs 240. 4 students among the group ...
  A: what is it?), Also, what is "Rs"? Anyhow...let x=the # of students who were supposed to go... ...
math word problems1/12/2008
  Q: uhm, hi! i was wonderimg if you could help me with these? a lot said that ur really good.. thanks.. ...
  A: ..what is it?), You have quite a list of questions! I'd rather not answer them all...it would take ...
dd1/11/2008
  Q: 1.prove that the equation ax2(square)+2hxy+by2(square)=0 represents a pair of straight lines passing ...
  A: 1. ax^2+2hxy+by^2=0...SOlving for y using the quadratic -- formuala: y=[-2hx(+ or -)sqrt(4h^2 x^2 ...
Math1/10/2008
  Q: Ashley O'Shaughnessy won $5000 in a contest. She invested some of the money at 5% simple interest ...
  A: Let x=the amount invested at 5%, then 2x-400=the amount invested at 6.5% Thus: (5% of x) + (6.5% of ...
math q1/5/2008
  Q: The sides of the large square are 16 cm. The midpoints of the sides are joined to form a new square. ...
  A: 1. do you mean the process (of joining midpoints and -- forming squares) is repeated until there are ...
taking 1000 or 10,000 steps1/4/2008
  Q: Lao Tzu wrote, "The journey of a thousand miles starts with a single step." Okay, it's all good! ...
  A: Depends on how long the step is! Suppose each step is x inches long, then the total ditance for ...
Ladder puzzle12/29/2007
  Q: In order to keep his 15' ladder from bowing, a painter uses a 6'x6'x6' cube, jammed up against the ...
  A: Sorry for the delay on this one...I needed a bit of time to type all of the following! I'll show ...
math equation12/26/2007
  Q: Please help with this problem. Two cyclists start biking from a trail’s start 3 hours apart. The ...
  A: The distance the 1st cyclist travels is 6(3+t) miles, and the distance the 2nd cyclist travles is ...
Word Problem ( Math )6/7/2007
  Q: you have just purchased new appliances worth $1900. you pay $700.00 down, and finance the remainder ...
  A: Wow, I just found this question of yours from the summer! I had "been on vacation" from AllExperts ...
work problems6/1/2007
  Q: A can do a piece of work in 10 days and B in 20 days. they work together ,but 2 days before the ...
  A: "A" can do 1/10 of the job per day, and "B" can do 1/20 of the job per day. So, if they work ...
Trig5/31/2007
  Q: An Egyptian pyramid has a square base and symmetrical sloping faces. The angle of inclination of a ...
  A: Use th Law of Sines to determine the length of s sloping face. The triangle formed has a base of ...
maths5/29/2007
  Q: i have 2 questions first there are 4 roads from A to B and 5 roads from B to C howm any possible ...
  A: 1. There are 4x5=20 ways to get from A to C...and 20 ways - to get back... 2. A square of area 36 ...
please help me out5/28/2007
  Q: 10 men & 6 children can complete a job in 2 days, 16 men and 16 children can complete the same job ...
  A: Let x=the rate at which one man can work (job/day) and y=the rate at which a child works (job/day) ...
Word Problem-is there an easier way?5/24/2007
  Q: I have a word problem that I can't figure out. Here it is- 'A girl went fishing. The first day she ...
  A: What you have there is what is called a series, that is the sum of terms that have a constant ratio ...
Business5/23/2007
  Q: Lotus Development has a software rental plan called SmartSuite that is available on the World Wide ...
  A: The compound interest formula is: A=P(1+r/n)^(n*t) So we get: A=2.99(1+0.01)^40 + 2.99(1+0.01)^39 + ...
Adult Tutoring Ideas?1/4/2007
  Q: Mr. Mantell, I am a safety professional working towards a National Certification (Certified Safety ...
  A: How about Sylvan? Check for other in your local Yellow Pages, under "tutoring" or "Education"... ...
Algebra word problem: time/distance/rate12/30/2006
  Q: Two airplanes leave a starting point traveling in the same direction, one at 550mph, the other at ...
  A: The answer I obtained can easily be verified: The faster plane travels: : 550 (miles/hr) X 18/37 ...
Algebra word problem: time/distance/rate12/28/2006
  Q: Two airplanes leave a starting point traveling in the same direction, one at 550mph, the other at ...
  A: Let x=the distance the faster plane has traveled let y=the distance the slower plane has traveled ...
How many possible combinations?1/9/2006
  Q: How many possible combinations are there in a 5 digit code using the numbers 1 through 6? Thanks!
  A: Do you mean "combinations" or "permutations"? Is repetition allowed? If it is a true code, like a ...
College Algebra9/19/2005
  Q: Need help with a word problem in algebra. A farmer spends $100 to buy 100 animals. Cows cost $10 ...
  A: OK, your equations are correct. Now let's solve for z, using 10x+5y+0.50z=100 So, z=200-20x-10y. ...
limits with brackets9/11/2005
  Q: What is the limit of [(x-2)] as x approaches 1.5? The answer is -1(as it says in the Kaplan AP ...
  A: The bracket notation is commonly used for "The Greatest Integer Function" - see this site for more ...
Sheep Pen9/9/2005
  Q: A sheep farmer had a sheep pen which was the shape of an equilateral triangle.The six sections he ...
  A: The area of an equilateral triangle, in terms of it's perimeter (P), is: A1=[sqrt(3)/36]P^2 The ...
question needs to be solved before friday.....pleeeeeaaase!!!9/7/2005
  Q: Here is a question i really need solved with explanation please. There are 16 boys in a class with ...
  A: The algebraic way is: Let x=the height of the new student. The total height of all the students ...
7 grade math9/6/2005
  Q: You have 4 pieces of gold chain with 3 links on each. If it costs $10.50 to break a link and $10.50 ...
  A: Well, I cannot draw a picture here...but I can explain it. The least expensive way is to use one of ...
Calculating force of water8/24/2005
  Q: I could probably resurrect some old books for this one, but do not have the time... I think it is ...
  A: This is a standard Calculus II problem..Here's how to solve it: One wall of the tank is 16' long by ...
Pacal's Triangle (Tower of Cubes)7/8/2005
  Q: A tower of cubes is made of 35 cubes in five layers. How many cubes are needed to form a similar ...
  A: The pattern is: 1 + 3 + 6 + 10 + 15 + ... That is: 1 + (1+2) + (1+2+3) + (1+2+3+4) + (1+2+3+4+5) + ...
asymptotes6/2/2005
  Q: What are the equations of all horizontal and vertical asymptotes for the curve y=x/(x(x^2-4))(the ...
  A: Vertical asymptotes occur where there is a division by zero...so, we solve x(x^2-4)=0, and get ...
%5/29/2005
  Q: Three years ago men made up two out of every three internet users in America. Today the ...
  A: Let x=the total number of Internet users 3 yrs ago. Thus, (2/3)x=the number of male Internet users 3 ...
From Pounds To Ounces5/27/2005
  Q: It is quite common to divide two numbers with like units. This type of division, if I'm not ...
  A: Doesn't the following: 4 ounces/16 ounces = 1/4, and doesn't this calculation represent how many 16 ...
From Pounds To Ounces5/26/2005
  Q: I want to thank you for the follow-up reply. Regarding number 2., How many 16 ounces are in 1/4 ...
  A: No, it would STILL NOT MAKE SENSE! If you are asking someone to calculate a number, it makes NO ...
From Pounds To Ounces5/25/2005
  Q: Can you explain why 1 and 2 do not make sense? I thank you for your follow-up reply.Hello: 1/4 ...
  A: 1. How many 16 ounces per pound are in 1/4 pounds? Does not make sense primarily because "16 ...
transformations1/21/2005
  Q: What is the equation of y=x^2 + 4 after: (a)a dilation of 2 (b)a rotation of 180 degrees (c)a ...
  A: a) dilaton in which direction...x or y? -- in y, it would be 2x^2+4 b) I'll assume rotations are ...
Ticket Problem1/16/2005
  Q: It's me again. I really wanna get this problems right so before test I'm well prepared. I wanna ...
  A: The first one- Let x=the # of times you ride the Ferris Wheel, and y=the # of times you ride the ...
Sequence1/13/2005
  Q: Me again, I just asked you the question.. what is the missing value in the following sequence: ...
  A: Oh yes, I am familiar with that website (http://www.research.att.com/~njas/sequences/)... and tried ...
word problem1/4/2005
  Q: as you ride the ferris wheel, the height above ground varies sinusoidally with time. the ferris ...
  A: Let the height above the ground be represented by h(t)=Asin(bt+c)+D So, A=41 ft (the radius of the ...
transformations1/2/2005
  Q: So why am I wrong?why do you have to reflect it in the x-axis first?Please go to this web site and ...
  A: OK, I somehow did not see (or notice) your minus sign on the 3! I thought you were doing the ...
transformations12/31/2004
  Q: Please go to this web site and look at number 31. ...
  A: No...You need to reflect (about x-axis) before the vertical shift of 3. So, one answer would be ...
Teeth on gears1/16/2004
  Q: This is a question from Brainbashers.com. I have a machine which has four cog wheels in constant ...
  A: Interesting question! What we need is the LCM (Least Common Multiple) of the 4 numbers: 242, 66, ...
Word problem for school, we are allowed to use any resource to figure out the solutions1/2/2004
  Q: This is the word problem: A town is replacing its water supply lines. The current system uses two ...
  A: Since volume of flow is cross-sectional area times the flow rate. I assume the problem is to find ...
algebra finance7/29/2003
  Q: An asset is purchased for $15,000 and depreciates at 12% per year. How long will it take to ...
  A: The value is given by, V(t)=$15,000(1-0.12)^t, t=# of years ==> V(t)=$15,000(0.88)^t, now solve for ...
Gallon Capacity7/26/2003
  Q: How would we figure out how many gallons an above ground round pool holds so we can figure out the ...
  A: The volume of a cylinder is pi*h*r^2, where h=height of water, and r=radius of the pool Convert the ...
Word Problem7/26/2003
  Q: Abe, Hi! I am stumped on two questions in my assignment and was wondering if you could help. Any ...
  A: 23. Let I=intensity, and x=distance. So, I=k/x^2, where k=constant of proportionality. When ...
water hoses7/11/2003
  Q: Two hoses are filling a swimming pool. The hose with the larger diamter supplies 1.5 times as much ...
  A: OOPS! Sorry, I pressed the wrong response before! Anyhow...Hello Charisma (is that your real ...
How to research?7/11/2003
  Q: How to research? --- I am a student in Computer Science department and I wonder how can I increase ...
  A: Wow, tough question to answer! In my opinion, when you learn (not just memorize facts, but actually ...
Algebraic Word Problem-Quadratic Systems6/13/2003
  Q: I have two algebraic word problems that have me stumped, and I would like you to help me solve them. ...
  A: 1. Let x be the base and y be the height... So, (1/2)xy=2a^2-2b^2, and x^2+y^2=4(2a^2+2b^2) ...
Word problems5/31/2003
  Q: I am currently homeschooling my two teenagers. I am pretty good with Algebra, but I just can't ...
  A: How about I show you the first one, and give you a chance to do the other...OK? Let x=the rate at ...
Word problem5/29/2003
  Q: One rental car agency charges $40 per day plus 15 cents per mile for a midsize car. Another agency ...
  A: Let m=# of miles driven... Agency 1: charges 40 + 0.15m dollars/day Agency 2: charges 45 + 0.10m ...
formula or pattern for rearrange letters or numbers.5/8/2003
  Q: I was wondering if there was a formauls for finding the number of ways something can be reaaranged ...
  A: There sure is! n distinct items can be arranged in n! ways (it's called "n factorial")...and ...
Help5/1/2003
  Q: It takes you 30 sec. to walk from the first floor of a building to the third floor. How long will it ...
  A: Since one must walk up 2 flights of stairs (from the 1st to 3rd floor), we assume a person can ...
word problem - yikes4/30/2003
  Q: I got this problem from my teacher because I needed an extra point for the week. But I think I'm ...
  A: Certainly the twins are the same age...so the worst pitcher and his/her twin are is also the same ...

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