At the city museum, child admission is $5.40 and adult admission is $8.90. On Monday, four times as many adult tickets as child tickets were sold, for a total sales of $1066.00. How many child tickets were sold that day?
The correct answer and explanation is :
Let’s solve the problem carefully step-by-step:
First, define variables:
- Let ( x ) = number of child tickets sold.
- Since four times as many adult tickets were sold, the number of adult tickets is ( 4x ).
Next, set up the equation based on the total sales:
- Child ticket price = \$5.40
- Adult ticket price = \$8.90
The total money earned from child tickets = ( 5.40x )
The total money earned from adult tickets = ( 8.90(4x) )
Since the total sales were \$1066.00, the equation is:
[
5.40x + 8.90(4x) = 1066
]
Simplify:
[
5.40x + 35.60x = 1066
]
[
41.00x = 1066
]
Now solve for ( x ):
[
x = \frac{1066}{41}
]
[
x = 26
]
Thus, 26 child tickets were sold that day.
Explanation (300+ words):
This problem is a classic example of setting up and solving a system involving relationships and totals. We are told that the adult tickets sold were four times the number of child tickets, and the total sales revenue is given.
The first step is to define what we don’t know. We let ( x ) represent the number of child tickets sold. Because there are four times as many adult tickets, the adult tickets are represented as ( 4x ).
Next, we relate the number of tickets sold to the amount of money made. Each child ticket brings in \$5.40, and each adult ticket brings in \$8.90. Therefore, the money from child tickets is ( 5.40x ), and the money from adult tickets is ( 8.90 \times 4x ) (which simplifies to ( 35.60x )).
Adding these together gives the total money earned: ( 5.40x + 35.60x ), which simplifies nicely to ( 41.00x ). Setting that equal to \$1066 (the total sales) gives the equation:
[
41.00x = 1066
]
To solve for ( x ), divide both sides by 41.00. Doing the division, we get:
[
x = 26
]
Thus, 26 child tickets were sold.
To verify, calculate:
- 26 child tickets = ( 26 \times 5.40 = 140.40 )
- 4 times 26 = 104 adult tickets
- 104 adult tickets = ( 104 \times 8.90 = 925.60 )
Adding:
[
140.40 + 925.60 = 1066.00
]
The verification confirms the answer is correct.
✅ Final Answer: 26 child tickets were sold.