TBIL-Precal Applications of Systems of Linear Equations (LF7)

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Section 3.7 Applications of Systems of Linear Equations (LF7)

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Objectives

Solve questions involving applications of systems of equations.

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Subsection 3.7.1 Activities

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Remark 3.7.1.

Now that we have explored multiple methods for solving systems of linear equations, let’s put those in to practice using some real-world application problems.

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Activity 3.7.2.

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Let’s begin by revisiting the carnival admission problem from Section 3.6.

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Admission into a carnival for

4

children and

2

adults is

$ 128.50 .

For

6

children and

4

adults, the admission is

$ 208 .

Assuming a different price for children and adults, what is the price of the child’s admission and the price of the adult admission?

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(a)

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First, set up a system of equations representing the given information. Use

x

to represent the child admission price and

y

for the adult admission price.

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${\begin{cases} x + y = 128.50 \\ x + y = 208 \end{cases}$
${\begin{cases} 2 x + 4 y = 128.50 \\ 4 x + 6 y = 208 \end{cases}$
${\begin{cases} 4 x + 2 y = 128.50 \\ 6 x + 4 y = 208 \end{cases}$
${\begin{cases} 6 x + 4 y = 128.50 \\ 4 x + 2 y = 208 \end{cases}$

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(b)

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Solve the system of equations.

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$(27, 10.25)$
$(15.25, 24.5)$
$(24.5, 15.25)$
$(10, 37)$

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(c)

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Write your solution in terms of the price of admission for children and adults.

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Activity 3.7.3.

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Let’s revisit another application we’ve encountered before in Section 1.2, Activity 1.2.7.

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Ammie’s favorite snack to share with friends is candy salad, which is a mixture of different types of candy. Today she chooses to mix Nerds Gummy Clusters, which cost

$ 8.38

per pound, and Starburst Jelly Beans, which cost

$ 7.16

per pound. If she makes seven pounds of candy salad and spends a total of

$ 55.61,

how many pounds of each candy did she buy?

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(a)

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Set up a system of equations to represent the mixture problem. Let

N

represent the pounds of Nerds Gummy Clusters and

S

represent the pounds of Starburst Jelly Beans in the mixture.

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${\begin{cases} N + S = 7 \\ 7.16 N + 8.38 S = 55.61 \end{cases}$
${\begin{cases} N + S = 7 \\ 8.38 N + 7.16 S = 55.61 \end{cases}$
${\begin{cases} N + S = 55.61 \\ 8.38 N + 7.16 S = 389.27 \end{cases}$
${\begin{cases} N + S = 7 \\ 7 N + 7 S = 55.61 \end{cases}$

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(b)

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Now solve the system of equations and put your answer in the context of the problem.

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Ammie bought $2.5$ lbs of Nerds Gummy Clusters and $4.5$ lbs of Starburst Jelly Beans.
Ammie bought $3.5$ lbs of Nerds Gummy Clusters and $3.5$ lbs of Starburst Jelly Beans.
Ammie bought $4.5$ lbs of Nerds Gummy Clusters and $2.5$ lbs of Starburst Jelly Beans.
Ammie bought $5.5$ lbs of Nerds Gummy Clusters and $1.5$ lbs of Starburst Jelly Beans.