A box contains 87 coins, only Dimes and nickels. The amount of money I the box is $5.45. How many dimes and how many nickels are in the box?

Write the situation as a simultaneous eqution:

x+y=87

10x+5y=545

Now solve for y by multiplying the whole of the first equation by the coefficient of x:

10x+10y=870

10x+5y=545

5y=325

y=65 nickels in the box

x+y=87

x=22 dimes in the box

To prove this is correct, we do (10 x 22) + (5 x 65) = 545 cents ($5.45)

There are 65 nickels and 22 dimes in the box.