could someone help me with this problem?

Question

Kelly has a collection of nickels, dimes and quarters with a total value of
$7.00 There are 7 more dimes than nickels and 3 times more quarters than nickels, how many of each coin does she have?

 

Kelly has ____ nickels, _____ dimes, and _____ quarters 

Answer 1

Hi Seth,

 

Let N = the number of nickels and D = the number of dimes and Q = the number of quarters

 

They have a total value of 700 cents--> 5N + 10D + 25Q = 700

 

There are 7 more dimes than nickels--> N + 7 = D

 

There are 3 times more quarters than nickels--> 3N = Q

 

Substitute N+7 for D in the first equation--> 5N + 10(N+7) + 25Q = 700

 

Substitute 3N for Q in that equation-->5N + 10(N+7) + 25(3N) = 700

 

5N + 10N + 70 + 75N = 700

 

90N = 630

 

N = 7

 

Then Q = 21 and D = 14

 

Make sure that their values add up to $7.00

 

Have fun.

 

Dan