Question

A purse containing $3.20 in quarters and dimes has, in all, 20 coins. Find the number of each kind of coin.

Answer 1

So Quarters (q) + Dimes (d) = 20

and .25q + .1(d) = 3.20

Answer 2

From here, we can solve for q or d.

q+d=20

So d=20-q

Answer 3

Now, we'll go into our second equation and solve it by replacing d with 20-q

So our problem looks like .25q +.1(20-q) = 3.20

Answer 4

I'll let you solve the rest.

But do you see how I set up both equations?

The number of quarters is unknown so I called it q.
The number of dimes is unknown so I called it d.

I know that the number of quarters plus the number of dimes is equal to 20, so my equation became q+d=20

Then, the value of a quarter is .25 so I multiply that by the number of quarters, giving me .25q.

Then, the value of a dime is .10 so I multiply that by the number of dimes, giving me .1d.

So .25q+.1d=3.20