Finding coins

Question

A collection of nickles and dimes is worth $9.45. If the number of dimes is doubled, the value is $16.65. Find the number of each coins 

Answer 1

Start by defining the unknowns:

 

number of nickels, N

number of Dimes, D

 

Write an equation for the amount of money

0.05N + 0.10D = 9.45

 

Now, if the number of Dimes, D is doubled

 

0.05N + 0.10(2D) = 16.65

0.05N + 0.20D = 16.65

 

Let's use elimination to solve for D. Subtract the two equations

 

 

 0.05N + 0.20D = 16.65

-0.05N - 0.10D = -9.45

     0  +  0.10D =  7.20

 

divide both sides by 0.10

 

D = 72 dimes

 

Put this back into one of the equations and solve for N, the number of nickels

 

0.05N + 0.10(72) = 9.45

0.05N + 7.20 = 9.45

0.05N = 9.45 - 7.20

0.05N = 2.25

N = 2.25/0.05

 

N = 45 nickels