Final answer:
A total of 25 child tickets were sold at that museum. It is determined by setting up a system of equations based on the cost of child and adult tickets and the total sales. Option E.
Step-by-step explanation:
The student is tasked with solving a system of equations to determine the number of child tickets sold at a city museum.
Let's call the number of child tickets c and the number of adult tickets a. The problem states that adult tickets cost $8.90 and child tickets cost $5.30.
It also provides that three times as many adult tickets as child tickets were sold, which can be expressed as a = 3c.
The total sales from the tickets were $800.00, which can be represented by the equation 5.30c + 8.90a = 800.
Substitute the expression for a from a = 3c into the total sales equation to get 5.30c + 8.90(3c) = 800.
Combining like terms gives us 5.30c + 26.70c = 800, which simplifies to 32c = 800. Dividing both sides by 32 yields c = 25, which means 25 child tickets were sold.
However, this number is not one of the options provided in the multiple-choice question.
Thus, we need to recheck our calculations.
Assuming the total sales and the ratio of adult to child ticket sales are correct, and keeping the same process of calculation, we again substitute 3c for a in the total equation. We have:
- 5.30c + 8.90(3c) = 800
- 5.30c + 26.70c = 800
- 32c = 800
- c = 800 / 32
- c = 25.
Hence, the right answer is option E.
The complete question is:
At the city museum, child admission is $5.30, and adult admission is $8.90. On Saturday, three times as many adult tickets as child tickets were sold, for a total sales of $800.00. How many child tickets were sold that day?
A. 50
B. 30
C. 20
D. 10
E. 25