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# Word Problems/to solve word problems using simultaneous linear equations

Question
HEY I'M ASTINA. AND I WOULD LIKE TO ASK SOME QUESTIONS.IT WILL BE A GREAT FAVOUR TO ME !

1.ONE - THIRD THE SUM OF 2 NOS. IS 6 WHILE HALF THEIR DIFF.IS ALSO 6 FIND THE NOS.

2.6 PENCILS & 4 ERASERS COST Rs42 WHILE 2 PENCILS AND 6 ERASERS COST Rs21. FIND THE PRICE OF A PENCIL AND AN ERASER.

3.THE PRICE OF BRUSHES IS Rs27 MORE THAN THE PRICE OF 3 PENCILS WHILE THE PRICE OF 3 BRUSHES AND 5 PENCILS IS Rs40. FIND THE PRICES OF ONE BRUSH AND ONE PENCIL.

4.A BOAT FIRST TRAVELS 48 KM DOWNSTREAM AND 24 KM UPSTREAM IN 7 HRS. THEN IT TRAVELS FOR 9 HRS , GOING 48 KM UPSTREAM AND 36 KM DOWNSTREAM. FIND THE SPEED OF THE BOAT IN STILL WATER AND THE SPEED OF THE WATER CURRENT.

Hello Astina,

1. Let x=the larger of the two numbers, and y=the smaller number.
...Thus, (x+y)/3=6 AND (x-y)/2=6...now solve these for x & y
==> multiplying the 1st equation by 3 gives: x+y=18
==> multiplying the 2nd equation by 2 gives: x-y=12
Now add the two equations so the y's drop out: 2x=30 ==> x=15 ==> y=3

2. Let p=the cost of a pencil, and e=the cost of an eraser
...Thus, 6p+4e=42 AND 2p+6e=21
==> multiplying the 2nd equation by -3 gives -6p-18e=-63,
so when we add the two the p's drop out ==> -14e=-21 ==> e=3/2=1.5 ==> p=6

3. Let b=the price of a brush, p=the price of a pencil
...Thus, b=3p+27 AND 3b+5p=40...now substitute b=3p+27 into the 2nd equation
and solve for p...3(3p+27)+5p=40 ==> 9p+81+5p=40 ==> 14p=-41 NEGATIVE???!!!
Hmm, looks like something is wrong here!  Are you sure you typed the problem
without error?

4. Let x=the speed of the boat in still water, y=the speed of the current.
...Thus, the speed of the boat downstream is x+y and upstream is x-y.
Now use distance = rate X time or time = distance/rate
The time required for the boat to go downstream 48 km is 48/(x+y).
The time required to go upstream 24 km is 24/(x-y).
But the total time is 7 hrs, so we get the equation: 48/(x+y) + 24/(x-y) = 7
Similarly, using the other information, we get: 48/(x-y) + 36/(x+y) = 9
Solving these two for x & y gives x=10 km/hr and y=2 km/hr.

Let me know if you need help getting those two answers.

I hope this helps!

TTYL, Abe

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment thanks for such an instant response

Word Problems

Volunteer

#### Abe Mantell

##### 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