A man has 20 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 275 cents, how many dimes & how many quarters

Question

How would I set this up?

Answer 1

Hi Candace!

 

A dime is worth 10 cents.

A quarter is worth 25 cents.

You want to write down what you know...and that is 2 different things:

 

So one equation would be        10D+ 25Q = 275, since 10 cents is from each dime, and 25 cents is from each quarter.  the total is 275 cents.

 

But you also know that you have 20 coins, so D + Q = 20    You need to write this in terms of either D or Q and plug it in the first equation.  D= 20 - Q then solve 10 (20 - Q) + 25Q = 275

 

Now it's all in terms of Q and you can solve for the number of quarters!  Once you have quarters, subtract from 20 to get the dimes:)