SOLUTION: In a collection of dimes and quarters, there are seven more quarters than dimes. How many dimes and quarters are there if the collection is worth $3.50? What is the equation for

Algebra ->  Equations -> SOLUTION: In a collection of dimes and quarters, there are seven more quarters than dimes. How many dimes and quarters are there if the collection is worth $3.50? What is the equation for       Log On


   

Question 126374: In a collection of dimes and quarters, there are seven more quarters than dimes. How many dimes and quarters are there if the collection is worth $3.50?
What is the equation for this?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The question should have been "what are the equations for this?"

You have a situation where you can express a relationship between the numbers of things and another relationship between the values of those things. Meaning that you will have to develop a system of equations and solve them.

Let q be the number of quarters and d be the number of dimes. The quantity relationship is q+=+d+%2B+7 because there are 7 more quarters than dimes.

Each quarter is worth 25 cents so the total value of q quarters in cents is 25q. Likewise for the dimes, the total value is 10d. We know that the total value of all the coins is $3.50 or 350 cents, so we can write:

25q+%2B+10d+=+350

Into this equation we can substitute the expression for the number of quarters in terms of dimes:

25%28d%2B7%29%2B10d=350
25d%2B175%2B10d=350
35d%2B175=350
35d=175
d=5

So there are 5 dimes. Since there are 5 dimes, there must be 5%2B7=12 quarters.

Check.
25%2A12=300
10%2A5=50
300%2B50=350