Question: 7. A adult tickets to the fair cost $25, and children's tickets cost $10. If a total of 1,000 people went to the fair last weekend, and the ticket seller made $16,825, how many children bought tickets to the fair?
• 4 adult tickets=25$
• A child's ticket=10$
a is the ticket price for an adult and c is for the ticket price for a child
An equation for the ticket for one adult is 25/4 = 6.25
If 1000 people went to the fair last weekends and the ticket seller made 16,825
6.25a + 10c = 16,825
a + c = 1000 multiply the equation by 10 so I can find c
10a + 10c = 1000
Graph shape: no visible graph; the visible math is a system of linear equations, positioned center-left.
1. **State the problem:** We want to find how many children bought tickets to the fair given that adult tickets cost $25, children's tickets cost $10, 1000 people attended, and total revenue was 16825.
2. **Define variables:** Let $a$ be the number of adult tickets sold and $c$ be the number of children's tickets sold.
3. **Write the system of equations:**
- Total people: $$a + c = 1000$$
- Total revenue: $$25a + 10c = 16825$$
4. **Solve the system:** From the first equation, express $a$:
$$a = 1000 - c$$
5. Substitute into the revenue equation:
$$25(1000 - c) + 10c = 16825$$
6. Distribute:
$$25000 - 25c + 10c = 16825$$
7. Combine like terms:
$$25000 - 15c = 16825$$
8. Subtract 25000 from both sides:
$$-15c = 16825 - 25000$$
$$-15c = -8175$$
9. Divide both sides by $-15$:
$$c = \frac{-8175}{-15}$$
$$c = \cancel{\frac{-8175}{-15}} = 545$$
10. **Answer:** The number of children who bought tickets is $\boxed{545}$.
11. **Check:** Adults $a = 1000 - 545 = 455$.
Revenue check:
$$25 \times 455 + 10 \times 545 = 11375 + 5450 = 16825$$ which matches the total revenue.