Question

A water park had 9081 visitors in June. The ratio of adult to children was 4 : 5. An adult ticket costs $10 and a child's ticket costs $8. In July the ticket prices increased to $15 for an adult and $11 for a child. The number of visitors fell to 7000 in July, split in the ratio 2 : 5, adults to children. The park manager thinks that sales had increased by more than 5%. Is he correct? Give a reason for your answer.

Answer 1

Yes, the manager is correct

Explanation:

In order to know this, we need to determine the total sale of the park in June and July for both adults and children.

In the month of june we have the following:

Visitors: 9081

Ratio A:C = 4:5

Adult ticket: 10$

Child ticket: 8$

So, if the ratio is 4:5, we can say that in 9 visitors, we have 4 adults and 5 child, therefore we can determine how many adults went in june:

If 4 adults --------> 9 people

Then X adults ---------> 9081 people

Solving for X:

X = 9081 * 4 / 9 = 4036 adults

This means that the number of child is:

C = 9081 - 4036 = 5045 childs

The total sales of the park in June would be:

T = (4036 * 10) + (5045 * 8) = 80,720$

This is the sale for the month of June. Let's apply the same procedure to the month of July, and then, we'll compare the sales and the percentage.

In the month of july we have the following:

Visitors: 7000

Ratio A:C = 2:5

Adult ticket: 15$

Child ticket: 11$

So, if the ratio is 2:5, we can say that in 7 visitors:

If 2 adults --------> 7 people

Then X adults ---------> 7000 people

Solving for X:

X = 7000 * 2 / 7 = 2000 adults

This means that the number of child is:

C = 7000 - 2000 = 5000 childs

The total sales of the park in June would be:

T = (2000 * 15) + (5000 * 11) = 85,000$

As we can see, the month of July was better, now, let's calculate the percentage of increase:

% = 85,000 - 80,720 / 85,000

% = 0.05035 * 100

% = 5.035%

Hence, we can conclude that the manager was right and it was a increase of more than 5% (But just for a pinch).

Hope this helps