At the city museum, child admission is $5.60 and adult admission is $8.80 . On Friday, twice as many adult tickets as child tickets were sold, for a total sales of $696.00 . How many child tickets were sold that day?
The correct answer and explanation is :
Let’s solve the problem step-by-step:
First, define variables:
- Let xx = number of child tickets sold
- Then, 2x2x = number of adult tickets sold (because twice as many adults as children)
The cost:
- Child ticket = $5.60
- Adult ticket = $8.80
The total sales equation is: 5.60x+8.80(2x)=696.005.60x + 8.80(2x) = 696.00
Simplify: 5.60x+17.60x=696.005.60x + 17.60x = 696.00 23.20x=696.0023.20x = 696.00
Solve for xx: x=696.0023.20x = \frac{696.00}{23.20} x=30x = 30
Thus, 30 child tickets were sold.
Full Explanation (around 300 words):
This problem involves setting up an equation based on a real-world situation. It’s important to define the unknowns clearly. Here, we are asked for the number of child tickets sold. Let’s represent that unknown by xx. Since the problem says there were twice as many adult tickets sold as child tickets, we know the number of adult tickets is 2x2x.
Next, the cost for each ticket is given: $5.60 for a child and $8.80 for an adult. So, the total money earned from child tickets would be 5.60×5.60x, and from adult tickets, it would be 8.80(2x)8.80(2x).
Adding both expressions gives the total revenue: 5.60x+8.80(2x)5.60x + 8.80(2x)
Multiplying 8.80×2×8.80 \times 2x gives 17.60×17.60x, so the expression simplifies to: 5.60x+17.60x=23.20×5.60x + 17.60x = 23.20x
Since the total sales were $696.00, set up the equation: 23.20x=696.0023.20x = 696.00
Now, solve for xx by dividing both sides by 23.20: x=696.0023.20=30x = \frac{696.00}{23.20} = 30
Thus, 30 child tickets were sold. If you want to double-check, you can calculate:
- 30 child tickets = 30×5.60=168.0030 \times 5.60 = 168.00
- 60 adult tickets (twice as many) = 60×8.80=528.0060 \times 8.80 = 528.00
- Total = 168.00+528.00=696.00168.00 + 528.00 = 696.00, which matches.