Agirl 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?show all

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