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. Set up variables for the number of tickets Let the number of adult tickets sold be represented as $a$. Since the ratio of child to adult tickets is $8:1$, the number of child tickets sold can be expressed as $c = 8a$.

2. Set up the equation based on the difference According to the problem, it is stated that the number of child tickets is 147 more than the number of adult tickets. This gives us the equation: $$ c = a + 147 $$

3. Substitute the expression for child tickets We can substitute $c$ with $8a$ from the earlier step into the equation we just formed: $$ 8a = a + 147 $$

4. Solve for $a$ Rearranging the equation to isolate $a$: $$ 8a - a = 147 $$ $$ 7a = 147 $$

Dividing both sides by 7: $$ a = \frac{147}{7} = 21 $$

5. Find the number of child tickets $c$ Now that we have found $a$, we can find $c$: $$ c = 8a = 8(21) = 168 $$

6. Calculate the total tickets sold To find the total number of tickets sold, we add the number of child and adult tickets: $$ \text{Total tickets} = a + c = 21 + 168 = 189 $$