How many dimes and quarters are there?

Question

A collection of dimes and quarters is worth $25. There are 40 more dimes than quarters. How many of each are there?

Answer 1

Let x be your number of dimes

Let y be your number of quarters.

 

The first statement tells you (and I will remove the decimals multiplying everything through by 10 for ease)

10x + 25y = 2500

 

The second statement tells you

x = 40 + y 

 

Since you have a value for x you can substitute it back into the first equation

10(40 + y) + 25y = 2500

400 + 10y + 25y = 2500

35y = 2100

y = 60 quarters

Knowing this and knowing you have 40 more dimes

x = 100 dimes

 

Check your math

100(10) + 60(25) = 2500

1000 + 1500 = 2500 so you are all set!