maribel has $1.25 in her pocket. The money is in quarters and dimes. There are a total of 8 coins. How many quarters and dimes does Maribel have in her pocket?

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.

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

x + y = 8   →   y = 8 - x     (1)

And the number of each type of coin times its value gives the total value

.25x + .10y =  1.25     (2)         put (1)  into (2)  for y

.25x + .10 [ 8 - x]  = 1.25         simplify

.25x + .80 - .10x  =  1.25

.15x + .80  = 1.25       subtract  .80  from each side

.15x  = .45      divide both sides by  .15

x = 3    this is the number of quarters

And using (1)     y =  8 - x   = 8 - 3  =   5   and this is the number of dimes