Chapter 6, Problem 14MCQ

a.

To determine

To define variables to represent the cost of an adult ticket and the cost of a child.

Answer to Problem 14MCQ

The cost for one adult for the admission in the museum is x.

The cost for one children for the admission in the museum is y.

Explanation of Solution

Given information :

The total cost for 4 adults and 2 children for admission in the museum is $110

The total cost for 4 adults and 3 children for admission in the museum is $123

Calculation :

Define the variable as below.

The cost for one adult for the admission in the museum is x

The cost for one children for the admission in the museum is y.

b.

To determine

To write a system of equations to find the cost of an adult ticket and a child.

Answer to Problem 14MCQ

  $4x+2y=110$ , $4x+3y=123$

Explanation of Solution

Given information :

The total cost for 4 adults and 2 children for admission in the museum is $110

The total cost for 4 adults and 3 children for admission in the museum is $123

Calculation :

The cost for one adult for the admission in the museum is x

The cost for one children for the admission in the museum is y

So according to question:

So the cost for 4 adults + the cost of 2 children= 110

Or $4x+2y=110$ …..Equation 1

And the cost for 4 adults + the cost of 3 children= 123

Or $4x+3y=123$ …..Equation 2

So the system of equations to find the cost of an adult ticket and a child are:

  $4x+2y=110$ ….. Equation 1

  $4x+3y=123$ .......Equation 2

c.

To determine

To solve the system of equations and explain the meaning of solution.

Answer to Problem 14MCQ

The cost for an adult for the admission in the museum is x = $ 21.

The cost for a child for the admission in the museum is y = $ 13.

Explanation of Solution

Given information :

The total cost for 4 adults and 2 children for admission in the museum is $110

The total cost for 4 adults and 3 children for admission in the museum is $123

Calculation :

The system of equations to find the cost of an adult ticket and a child are:

  $4x+2y=110$ ….. Equation 1

  $4x+3y=123$ .......Equation 2

Using elimination method:

Subtracting Equation 2 from Equation 1, we get:

  $\begin{array}{l}(4x+3y)-(4x+2y)=123-110\\ \Rightarrow 4x+3y-4x-2y=13\\ \Rightarrow 3y-2y=13\\ \Rightarrow y=13\end{array}$

Putting the value of the y in the Equation 1:

  $\begin{array}{l}4x+3\times 13=123\\ \Rightarrow 4x+39=123\\ \Rightarrow 4x=123-39\\ \Rightarrow 4x=84\\ \Rightarrow x=\frac{84}{4}\\ \Rightarrow x=21\end{array}$

So, the cost for an adult for the admission in the museum is x = $ 21

And the cost for a child for the admission in the museum is y = $ 13.

d.

To determine

To write the mathematical practice that was used.

Answer to Problem 14MCQ

Solving system of linear equations by Elimination.

Explanation of Solution

Given information :

The total cost for 4 adults and 2 children for admission in the museum is $110

The total cost for 4 adults and 3 children for admission in the museum is $123

Calculation :

The system of equations is solved by eliminating the variables. So, the mathematical practice used was Solving system of linear equations by Elimination.

e.

To determine

To find the charge for 3 adults and 5 children for the admission in the museum.

Answer to Problem 14MCQ

The total charge for 3 adults and 5 children for the admission in the museum is $128.

Explanation of Solution

Given information :

The total cost for 4 adults and 2 children for admission in the museum is $110.

The total cost for 4 adults and 3 children for admission in the museum is $123.

Calculation :

The cost for an adult for the admission in the museum is x = $ 21.

The cost for a child for the admission in the museum is y = $ 13.

The total charge for 3 adults and 5 children for the admission in the museum:

3 $\times$ Adult charge + 5 $\times$ Children charge

  $\begin{array}{l}=3\times 21+5\times 13=63+65\\ =128\end{array}$

The total charge for 3 adults and 5 children for the admission in the museum is $128.