Morgan has three times as many pennies as quarters. If Morgan had three more quarters and seventeen fewer pennies, she would have the same number of each coin. How much money does she have?

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Answer 1 · 2016-11-28T01:02:03

$2.80

Let's have #p="number of pennies"# and #q="number of quarters"#.

We're told that Morgan has three times as many pennies as quarters, so

#p=3q#

we're also told that if she had three more quarters and seventeen fewer pennies, there would be the same number of coins, so I can write:

#p-17=q+3#

Now let's solve! I'm going to substitute the first equation into the second:

#p-17=q+3#

#(3q)-17=q+3#

and now solve for #q#:

#2q=20#

#q=10#

and now let's find #p# - we can substitute back into either of the original equations (I'll do both to show the answer is the same):

#p=3q#

#p=3(10)=30#

and

#p-17=q+3#

#p-17=10+3#

#p=30#

Now to the final part - how much money does Morgan have? 30 pennies at 1 cent each and 10 quarters at 25 cents each gives us:

#30($0.01)+10($0.25)=$0.30+$2.50=$2.80#