Q. 4.47 - Intermediate Algebra

Question

Translate to a system of equations and solve:

The ticket office at the zoo sold $553$tickets one day. The receipts totalled $\backslash (3936$. How many $\backslash )9$ adult tickets and how many $6 child tickets were sold?

Step-by-Step Solution

Answer

The number of adult tickets sold$=206$

The number of child tickets sold$=347$

Step 1. Given Information.

• The total amount is $\$3936$.
• The total number of tickets sold is $553$ tickets.  
• The price of the tickets for adults is $\$9$ and the price of the tickets for children is $\$6$

Step 2. Form the equations

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

The total tickets are $553$.

According to the question

$x+y=553\_\_\_\_\left(1\right)$

Now,

The price of adult tickets is $\$9$ and child tickets is $\$6$.

According to the question,

$9x+6y=3936\_\_\_\_\_\left(2\right)$

Step 3. Solve the equations by elimination method

Multiplying equation $\left(1\right)$ by $6$, we get:

$$\begin{gathered} 6x+6y=553\times 6 \\ 6x+6y=3318\_\_\_\_\left(3\right) \end{gathered}$$

Now, subtracting equation $\left(3\right)$ from equation $\left(2\right)$, we get:

$$\begin{gathered} 9x+6y-(6x+6y)=3936-3318 \\ 9x-6x=618 \\ 3x=618 \end{gathered}$$

Dividing $3$ into both sides, we get:

$$\begin{gathered} \frac{3x}{3}=\frac{618}{3} \\ x=206 \end{gathered}$$

Step 4. Substitute the value x in 1 to get y

Substitute the value $x=206$ in equation $\left(1\right)$ , we get:

$$\begin{gathered} x+y=553 \\ 206+y=553 \end{gathered}$$

Subtracting $206$ from both sides we get:

$$\begin{gathered} 206+y-206=553-206 \\ y=347 \end{gathered}$$

So, the number of adults tickets sold is $206$ and the number of child tickets sold is $347$.