Question

Sue has 100 dimes and quarters. If the total value of the coins is $21.40, how many of each kind of coins does she have?

X=?
Y=?

Show your work please

Answer 1

There would be 24 dimes and 76 quarters.

Explanation:

In order to find this, start by defining the number of dimes by x and the number of quarters as y. Now we can create a system of equations. Make the first about the total number of coins.

x + y = 100

Make the second about the amount of money.

.10x + .25y = 21.40

Now we can solve using elimination by multiplying the second equation by -4 and adding through.

x + y = 100

-.40x - y = -85.60

-----------------------

.60x = 14.4

x = 24

Now we can use the amount of dimes we have to find the number of quarters.

x + y = 100

24 + y = 100

y = 76