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

Answer:

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"#.