The document discusses using systems of equations to solve real-world problems. It gives examples of using a system to determine how many coins are in a piggy bank or how many party supplies can be purchased with a budget. It then works through setting up and solving a system to determine how many fill-in-the-blank and multiple choice questions are on a 25 question, 100 point test if fill-in questions are worth 3 points and multiple choice questions are worth 8 points. The solution is that there are 20 fill-in questions and 5 multiple choice questions. It concludes by posing a similar problem for the reader to solve.

1. Systems of
Equations in the
Real World!
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2. Did you know that you can use a system of
equations to solve problems in the real world?
For instance you could
use a system to find
out how many dimes
and nickels are
in a piggy bank!
Or you can use a system
to figure out how many
balloons and packs of
streamers you can buy
for a birthday party if
you only have so much
money to spend!
Let’s take a look at using a system to solve a real world problem!
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3. A test with 25 questions is worth 100 points. Some of
the questions are fill in the blank and some of the
questions are multiple choice. If a fill in the blank
question is worth 3 points and a multiple choice
question is worth 8 points, how many questions of each
type are on the test?
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Assign a variable to represent the two types of questions.
x = the number of fill in the blank questions and y = the number of multiple choice questions
Put the information into a chart to organize it.
Question
Fill in
the
Blank
Multiple
Choice
Total
Number
of each
Type
x
y
25
Point
Value
3x
8y
100

4. Question
Fill in
the
Blank
Multiple
Choice
Total
Number
of each
Type
x
y
25
Point
Value
3x
8y
Now that everything is organized in the chart,
you can write the system of equations you
need to solve in order to find how many of
each type of question is on the test.
x + y = 25
3x + 8y = 100
100
Now let’s solve the system using elimination.
Multiply the first
equation by -3 so that
the x’s will cancel.
x + y = 25
3x + 8y = 100
x + 5 = 25
-5 -5
x = 20
-3x + -3y = -75
3x + 8y = 100
5y = 25
5
5
y=5
Divide by 5.
Now find x by substituting
5 in for y and solve.
Now we have the answer to the original
question: there are 20 fill in the blank
questions and 5 multiple choice question
on the test.

5. Okay, now it’s your turn!
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A test with 30 questions is worth 100 points.
Some of the questions are true/false and some
of the questions are multiple choice.
If a true/false question is worth 4 points and a
multiple choice question is worth 3 points, how
many questions of each type are on the test?
Remember:
Assign variables
Put the information in a chart
Write the system
Solve the system
Write your answer in a complete sentence

6. Written
by
Genny Simpson
2/18/2014