Question

A girl has $3.35 in her pocket, consisting of dimes and quarters. If there are 23 coins in all, how many of each does she have

Answer 1

Answer:

7 quarters

16 dimes

Step-by-step explanation:

Represent

d=number of dimes

q=number of quarters

thererfor

q+d=23

1q=0.25

1d=0.10

therefor

total value=3.35=0.25q+0.1d

so we have

q+d=23

0.25q+0.1d=3.35

solve

q+d=23

subtract q from both sides

d=23-q

subsitute

0.25q+0.1(23-q)=3.35

distribute

0.25q+2.3-0.1q=3.35

group like terms

0.25q-0.1q+2.3=3.35

add like terms

0.15q+2.3=3.35

subtract 2.3 from both sides

0.15q=1.05

multipliy both sides by 100 to get rid of decimal

15q=105

divide both sides by 15

q=7

subsitute

q+d=23

7+d=23

subtract 7

d=16

7 quarters

16 dimes