Kristen has 64 coins in her bank. she has $9.25 in dimes and quarters. how many dimes and quarters does she have?

D= # of dimes
q= # of quarters

QUANTITY EQUATION:
d + q= 64

COST EQUATION:
0.10d + 0.25q= $9.25

STEP 1:
multiply quantity equation by -0.10 to be able to eliminate the d term in step 2

(-0.10)(d + q)= (-0.10)(64)
-0.10d - 0.10q= -6.40

STEP 2:
add equation from step 1 to cost equation to eliminate the d term and solve for q

Add
0.10d + 0.25q= $9.25
-0.10d - 0.10q= -6.40

0.15q= 2.85
divide both sides by 0.15

q= 19 quarters

STEP 3:
substitute q value in step 2 into either original equation to find d value

d + q= 64

d + 19= 64
subtract 19 from both sides

d= 45 dimes

CHECK:
0.10d + 0.25q= $9.25
0.10(45) + 0.25(19)= 9.25
4.50 + 4.75= 9.25
9.25= 9.25

ANSWER: There are 45 dimes and 19 quarters.

Hope this helps! :)