How many of each type of coin do they​ have?

Question

Kevin and Randy Muise have a jar containing 62 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $7.90. How many of each type of coin do they have?

Answer 1

Let q = quarters and n = nickels

Here's what we know:

q + n = 62 (there are 62 coins of either quarters or nickels)

.25q + .05n = 7.9 (the total value of these coins is $7.90)

 

We can solve this one of two ways: we can either use substitution by moving one of the variables in the first equation to the other side via subtraction, or we can multiply the second equation by -4 and use elimination. For this problem, I'll use the latter:

 q  +  n = 62

-q - .2n = -31.6

-------------------

.8n = 30.4

 

Divide both sides by .8:

n = 38

 

Now that we know nickels, we can find quarters:

q + 38 = 62

q = 24

 

Check:

24 * .25 + 38 * .05 = 7.9

6 + 1.9 = 7.9