Expert: Sherry Wallin - 12/1/2008

Question
Hello homeschool parent again I dnt know anything about word problems so please could u do step by step for me the cirriculum still has not sent the answer and they told me to come here please help me god bless





Solve the following word problems by setting up and equation. Show all work.

1. Sara and Elizabeth went shopping together at their favorite store during a sale. They both bought some dress shirts that cost $25.00 apiece and t-shirts that cost $10.50 apiece. If Sara bought 3 more dress shirts than Elizabeth and they both bought 4 t-shirts, how many dress shirts did Sara buy if together they spent a total of $309.00 (before taxes) on these items

2. A military plane carrying heavy cargo can fly at and average rate of 400mph. Another military plane carrying soldiers can fly at an average rate of 600mph. Both planes leave the same airbase and are headed to the same destination for a military operation. If the cargo plane took two and a half hours longer to arrive at the destination than the plane carrying the soldiers, then how far is the destination?

3. A stuntman built a ramp in the shape of a right triangle. If the base of the ramp is 12 feet long and the length of the incline is 6 feet longer than the height, then what is the height of the ramp?

4. Brian has a total of 241 dimes and nickels.  If he has $15.65 total in dimes and nickels, then how many nickels does he have?

5. The sum of two positive integers is 1,287. If the larger number is 9 1/2 more than 2 1/2 times the smaller number, then what are the two numbers?

Answer
I am going to start with #5 because it is a standard word problem in algebra using a system of linear equations. Choose one of the unknown values and call it x, say x = larger integer,then call the smaller integer y. The relationship is given for the sum so x   y = 1287 is one of the equations. The other equation is created from the relationship:
"the larger number is 9.5 more than 2.5 times the smaller number"
x = 9.5   2.5y

so the system is x   y = 1287 solve for

x = -y   1287 = 1287 - y
x = 9.5   2.5y  (*)and subtract the 2nd from the first getting

x = 1287 -y
-x = -9.5 -2.5y notice the sign change from (*) above
_______________
0*x = 1277.5 - 3.5y  now solve for y: 1277.5/3.5 = 365 = y
plug in this value of y into either equation to find x, I used
x = 1287 -y so = 1287-365 = 922

What have we found here? We have found a simultaneous solution to both equations for both variables

The larger number is 922 and the smaller number is 365
You can check this answer for xand y in both of the equations above.

This is it for now. I will add to this later.

Math Prof