A student makes a 9.25 purchase at the bookstore with a $20 bill. The store has no bills and gives the change in quarters and fifty-cent pieces. There are 30 coins in all. How many of each kind are there?

1 Answer
MathFact-orials.blogspot.com
Nov 20, 2016

#"Quarters"=17, "Fifty-cent pieces"=13#

Explanation:

The student is going to get $10.75 of change ($20-$9.25=$10.75) and we get Quarters and Fifty-cent pieces. I'll assign Q for the number of quarters and F for the number of fifty-cent pieces.

We know two things:

#Q+F=30# - there are 30 coins in total and
#Q(.25)+F(.5)=10.75# - the total change comes to 10.75.

Now let's solve for Q and F:

#Q=30-F# - let's substitute this into the other equation:

#(30-F)(.25)+F(.5)=10.75#

Before I distribute this out, I'm going to multiply both sides by 4 to get rid of the decimals:

#4((30-F)(.25)+F(.5))=4(10.75)#

#4(30-F)(.25)+F(4)(.5))=4(10.75)#

#(30-F)+2F=43#

#F=13#

which means

#Q+13=30#

#Q=17#

Does this work? Let's check:

#17(.25)+13(.5)=10.75#

#4.25+6.5=10.75#

#10.75=10.75#

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