Abox 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.