q=quarters, d=dimes
q+d=8
.25q+.1d=1.25
Let's set the first equation to equal d.
d=8-q
.25q+.1(8-q)=1.25
Distribute.
.25q+.8-.1q=1.25
Combine Like Terms
.15q+.8=1.25
Subtract .8
.15q=.45
Divide by .15
q=3
Now, let's solve for d in the first equation.
d+3=8
Subtract 3, and you get d=5
So, there are 5 dimes and 3 quarters in Maribel's pocket.
Check: .25(3)+.1(5)=1.25
.75+.5=1.25
1.25=1.25 which is true.
