An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on... An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets than adult tickets. How many tickets did the amusement park sell on Saturday? Read more

Steps to Solve

1. Define Variables Let $c$ be the number of child tickets sold and $a$ be the number of adult tickets sold.

2. Set Up Equations Based on the Problem From the ratio given (8:1), we can express $c$ in terms of $a$: $$ c = 8a $$

3. Incorporate the Additional Information We know that the amusement park sold 147 more child tickets than adult tickets: $$ c = a + 147 $$

4. Substitute the First Equation into the Second Now we can substitute the first equation into the second: $$ 8a = a + 147 $$

5. Solve for $a$ Subtract $a$ from both sides: $$ 8a - a = 147 $$

This simplifies to: $$ 7a = 147 $$

Now, divide both sides by 7: $$ a = \frac{147}{7} $$ $$ a = 21 $$

6. Find the Number of Child Tickets Now that we have $a$ (the number of adult tickets), substitute it back to find $c$: $$ c = 8a = 8 \cdot 21 = 168 $$

7. Calculate Total Tickets Sold Add child and adult tickets to find the total tickets sold: $$ \text{Total Tickets} = c + a = 168 + 21 = 189 $$