Lucy has 34 coins consisting of nickels and quarters amounting to $2.90. How many coins of each kind does she have?

1 Answer
Mar 22, 2018

Lucy has "6 quarters" and "28 nickels"

Explanation:

I am going to give nickels and quarters their own variable. Nickels will be n and quarters will be q. Since Lucy has 34 coins total, we can make this equation:
n + q = 34

The second part is about the value of the coins. Since nickels are worth 5 cents (or 5/100 of a dollar) and quarters are worth 25 cents (or 25/100 of a dollar), we can make this equation:

0.05n + 0.25q = 2.90

I'm actually going to multiply this whole equation by 100, to move the decimal points two places and make this easier to solve:

5n + 25q = 290

Now we will rearrange the first equation to solve for one variable:
n + q = 34
n = 34 - q

Substitute that into the second equation and solve for q

5n + 25q = 290
5(34 - q) + 25q = 290
170 - 5q + 25q = 290
170 + 20q = 290
20q = 120
q = 6

Lucy has "6 quarters". Now substitute q into the first equation to solve for n.
n = 34 - q
n = 34 - 6
n = 28

She has "28 nickels".