nickles and dimes

Question

Abel saved 43 more nickles than dimes. After he spent 17 dimes, he had twice as many nickles than dimes. How many coins did he have left?

Answer 1

Let N = number of nickels (no nickels spent)

     D = number of dimes initially saved

     D' = number of dimes left after spending

 

1)  N = D + 43

2)  D' = D - 17

3)  N = 2*D' = 2*(D - 17)

 

Set equations 1) and 3) equal to each other and solve for D:

 

D + 43 = 2*(D - 17)

 

D + 43 = 2*D - 34

 

D = 43 + 34 = 77

 

N = D + 43 = 77 + 43 = 120 nickels left

 

D' = D - 17 = 77 - 17 = 60 dimes left

 

Total coins left = 120 + 60 = 180 coins