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

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) (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 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:

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

So there are 5 dimes. Since there are 5 dimes, there must be quarters.

Check.

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