Q10. - Algebra 1

Question

GRIDDED RESPONSE Mr. Branson bought a total of 9 tickets to the zoo. He bought children tickets at the rate of \(6.50 and adult tickets for \)9.25 each. If he spent $69.50 altogether, how many adult tickets did Mr. Branson purchase?

Step-by-Step Solution

Answer

Mr. Branson purchased 4 adult tickets.

Step 1. Write information in terms of equation.

Let the number of children tickets be x and the number of adult tickets be y, such that, 

$$\begin{gathered} x+y=9 \\ y=9-x \end{gathered}$$

 

Therefore, the equation for total expense is

$6.50x+9.25y=69.50$

Step 2. Replace variables with values.

Replace y with $9-x$ in $6.50x+9.25y=69.50$.

$$\begin{gathered} 6.50x+9.25\left(9-x\right)=69.50 \\ 6.50x+83.25-9.25x=69.50 \\ -2.75x=-13.75 \\ x=5 \end{gathered}$$  

Therefore, number of children ticket is 5.

Step 3. Find the number of adult tickets.

Replace x with 5 in $y=9-x$.

$$\begin{gathered} y=9-x \\ =9-5 \\ =4 \end{gathered}$$

Therefore, number of adult tickets is 4.