Question

When Julie dumped out the big jar of nickels and dimes, she found 222 coins. If there was $19.80 in the jar, how many of each kind of coin was there?

Answer 1

The jar contained 174 dimes and 48 nickels.

Explanation:

To solve this problem, you're going to have to write two equations, one that relates the number of each type of coin with the total number of coins found in the jar, and the other that relates the value of these coins with the total value.

Let's say that the jar contained `x` dimes and `y` nickels. Your first equation is

`x + y = 222`

Your second equation will be

`0.10 * x + 0.05 * y = 19.80`

Use the first equation to write `x` as a function of `y`

`x = 222-y`

Now use this in the second equation to find the value of `y`

`0.10 * (222-y) + 0.05y = 19.80`

`22.2 - 0.10y + 0.05y = 19.80`

`-0.05y = -2.4 implies y = 2.4/0.05 = color(green)("48 nickels")`

This means that the jar also contained

`x = 222 - 48 = color(green)("174 dimes")`