Q 4.48 - Intermediate Algebra

Question

Translate to a system of equations and solve:

The box office at a movie theater sold $147$ tickets for the evening show, and receipts totaled $\backslash (1302$. How many

$\backslash )11$ adult and how many $\$8$ child tickets were sold?

Step-by-Step Solution

Answer

The number of adult tickets sold for the movie$=42$

The number of adult tickets sold for the movie$=105$

Step 1. Given information

• The total amount is $\$1302$.
• The total number of movie tickets sold is $147$ tickets.  
• The price of the tickets for adults is $\$11$and the price of the tickets for children is $\$8$

Step 2. Form the equations

Let the number of adults tickets for the movie be $x$and the number of child tickets for the movie be $y$ .

The total tickets are $147$.

According to the question,

$x+y=147\_\_\_\_\left(1\right)$

Now,

The price of adult tickets is $\$11$ and child tickets is $\$8$

According to the question,

$11x+8y=1302\_\_\_\_\left(2\right)$

Step 3. Solve the equations by elimination method

Multiplying equation $\left(1\right)$ by $11$ we get:

$$\begin{gathered} 11x+11y=147\times 11 \\ 11x+11y=1617\_\_\_\left(3\right) \end{gathered}$$

Subtracting the equation $\left(3\right)$ from equation $\left(1\right)$, we get:

Dividing both sides by $3$ , we get:

$$\begin{gathered} \frac{3y}{3}=\frac{315}{3} \\ y=105 \end{gathered}$$

Step 4. Substitute the value of y in equation 1

Substituting the value $y=105$ in the equation $\left(1\right)$, we get:

$$\begin{gathered} x+y=147 \\ x+105=147 \end{gathered}$$

Subtracting both sides from$105$, we get:

$$\begin{gathered} x+105-105=147-105 \\ x=42 \end{gathered}$$

So, the number of adults tickets sold for the movies is $42$ and the number of child tickets sold for the movie is $105$.