Question

A coin bank contains $12.45 in quarters and dimes. If there are 16 more dimes than quarters, how many are there of each?​

Answer 1

Answer is
Dimes = 47
Quarters = 31

Step by step

Dimes =.10
Quarters = .25

Dimes = q + 16
Quarters = q

Equation is .25q + .10d = $12.45
Substitute value of dimes in for d

.25q + .10( q + 16 ) = 12.45
Multiply

.25q + .10q + 1.6 = 12.45
Simplify

.35q + 1.6 = 12.45
Subtract 1.6 from both sides to isolate q

.35q + 1.6 - 1.6 = 12.45 - 1.6
Simplify

.35q = 10.85
Divide both sides by .35 to solve for q

.35/.35q = 10.85/.35
Simplify

q = 31
Quarters = 31

Now sub value of q into equation for dimes

Dimes = q + 16

Dimes = (31) + 16

Dimes = 47

Check your work

Dimes = .10 x 47 = $4.70
Quarters = .25 x 31 = $7.75

Total money = $12.45

Problem solved