Your piggy bank contains $19.75 in dimes and quarters. there are 100 coins in all. how many dimes are there?

Let x = be the number of dimes and y = number of quarters. 

Since the total number of coins is 100, x + y = 100. 

Since the total is cent value is 19.75, comprised of .10 for dimes and .25 for quarters, we have .10x + .25y = 19.75. 

This is just a system of equations. Solve one of the dozen ways that work for solving systems of linear equations. 

Using substitution: 

x = 100 - y 

Plug this into the other equation 

.10 (100 - y) + .25 y = 19.75 

10 - .10 y + .25 y = 19.75 

10 + .15y = 19.75 

.15 y = 9.75 

y = 65 

So there are 65 quarters. Since x + y = 100, there must be 35 dimes.Hope This Helps

D = no. of dimes
q = no. of quarters

$total equation
.10d + .25q = 19.75

No. of coins equation
d + q = 100
d = (100-q)

Replace d
with (100-q) in the $total equation
.10(100-q) + .25q = 19.75
10 - .10q + .25q = 19.75

10.15 q = 9.75
q = 
q = 65 quarters

100 - 65 =

35 dimes.