Help with the question below

Question

Student has $4.50 in change. He has four more quarters than dimes. Three times as many nickels as dimes. How many of each coin? I keep getting 6.363636 so I'm doing something wrong

Answer 1

First, we need to see that 4 quarters more than the number of dimes is $1.00

 

The, let x = number of dimes,  x + $1.00  = number of quarters, and 3x = number of nickels

 

Our equation will be x + (x + $1.00) + 3x = $4.50

Expanding, we get 5x + $1.00 = $4.50, and then 5x = $3.50

So, the number of dimes will be 7, 11 quarters and 21 nickels

 

Proof, each dime = $0.10, so ($0.10 x 7 ) + ($0.10 x 7) + $1.00 + ($0.10 x 21 ) = $4.50; $0.70 + $0.70 + $1.00 + $2.10 = $4.50