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?
Understand the Problem
The question is asking how many tickets the amusement park sold on Saturday, given that the ratio of child to adult tickets is 8:1, and they sold 147 more child tickets than adult tickets.
Answer
The amusement park sold a total of 189 tickets on Saturday.
Answer for screen readers
The amusement park sold a total of 189 tickets on Saturday.
Steps to Solve
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Define Variables Let $c$ be the number of child tickets sold and $a$ be the number of adult tickets sold.
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Set Up Equations Based on the Problem From the ratio given (8:1), we can express $c$ in terms of $a$: $$ c = 8a $$
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Incorporate the Additional Information We know that the amusement park sold 147 more child tickets than adult tickets: $$ c = a + 147 $$
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Substitute the First Equation into the Second Now we can substitute the first equation into the second: $$ 8a = a + 147 $$
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Solve for $a$ Subtract $a$ from both sides: $$ 8a - a = 147 $$
This simplifies to: $$ 7a = 147 $$
Now, divide both sides by 7: $$ a = \frac{147}{7} $$ $$ a = 21 $$
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Find the Number of Child Tickets Now that we have $a$ (the number of adult tickets), substitute it back to find $c$: $$ c = 8a = 8 \cdot 21 = 168 $$
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Calculate Total Tickets Sold Add child and adult tickets to find the total tickets sold: $$ \text{Total Tickets} = c + a = 168 + 21 = 189 $$
The amusement park sold a total of 189 tickets on Saturday.
More Information
This problem demonstrates how to set up and solve a system of equations based on a ratio and additional conditions. The ratio of tickets sold can often lead to valuable algebraic insights and efficient problem-solving strategies.
Tips
- Misinterpreting the Ratio: Ensure that the ratio is understood correctly (child tickets to adult tickets).
- Ignoring the Additional Information: It's essential to combine all the given relationships in the problem to form correct equations.
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