James has 33 coins in his pocket, all of them nickels and quarters. If he has a total of $2.25, how many quarters does he have?

1 Answer
Mar 19, 2018

Answer:

James has #"3 quarters"#

Explanation:

I'm going to give nickels and quarters their own variable. Nickels will be #n# and quarters will be #q#. Since he has #"33 total"# we can write this equation:
#n + q = 33#

The second part is about the #"value"# of the nickels and quarters. Since nickels are worth #"5 cents"# and quarters are worth #"25 cents"# we can make this equation:

#0.05n + 0.25q = 2.25#

I'm actually going to multiply this whole equation by #100# to move the decimal point 2 places and make it easier to solve:

#5n + 25q = 225#

We need to find how many #"quarters"# he has, so we need to leave #q# in the equation so that we can solve for it. So let's rearrange the first equation:
#n + q = 33 rarr n = 33 - q#

Now substitute it into the second equation:
#5n + 25q = 225#

#5(33 - q) + 25q = 225#
#165 - 5q + 25q = 225#
#165 + 20q = 225#
#20q = 60#
#q = 3#