SOLUTION: John wants to buy something for himself with his pocket money. He has a budget of $105 to spend on $25 T-shirts, $10 CDs, $5 books. He wants to buy 10 items and wants to buy as man

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: John wants to buy something for himself with his pocket money. He has a budget of $105 to spend on $25 T-shirts, $10 CDs, $5 books. He wants to buy 10 items and wants to buy as man      Log On


   

Question 1095496: John wants to buy something for himself with his pocket money. He has a budget of $105 to spend on $25 T-shirts, $10 CDs, $5 books. He wants to buy 10 items and wants to buy as many books as T-shirts and CDs combined.
How many of each item should he buy? Write a system of equations to help you solve this problem.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!

Let t = T-shirts, c = CDs, and b = books

t%2Bc%2Bb+=+10 the number of items is 10
25t%2B10c%2B5b+=+105 the total cost ($25 for a T-shirt, $10 for a CD, $5 for a book) is 105
t%2Bc+=+b the number of books is equal to the combined number of T-shirts and CDs

I'll let you solve the system of equations to find the answer to the problem.

Note that the first and last equations together immediately give you the number of books; then substituting that number into the first and second equations gives you a system you can solve to find t and c.