The manager of the ice cream shop noticed that 90% of all club
members brought along a family member who spent an average
of $18 in the shop. The tax on their bill was 5.5%.
a.
What was the total amount spent by the family members in one
year?
b.
What would each family member have to spend, on average, to
generate $5,000 in income before sales tax?
c.
What would each family member’s average bill be with sales
tax?
To answer these questions, we need to break down the information and use some calculations.
a. What was the total amount spent by the family members in one year?
Step 1: Find the average amount spent by each family member.
From the information given, we know that each family member spent an average of $18.
Step 2: Calculate the total amount spent by the family members.
Since 90% of all club members brought along a family member, we can assume that this percentage applies to the total number of club members. Let's call the total number of club members "x".
The total amount spent by the family members in one year would be x * 0.9 * $18.
b. What would each family member have to spend, on average, to generate $5,000 in income before sales tax?
Step 1: Calculate the amount before sales tax for each family member.
Since the tax on their bill was 5.5%, we can assume that their total bill was 100% + 5.5% = 105.5% of the amount before tax.
Let's call the average amount each family member needs to spend "y".
The amount before tax is y, and the total bill after tax is y * 105.5%.
So, y * 105.5% = $5,000.
Step 2: Solve for y.
Divide both sides of the equation by 105.5% to isolate y:
y = $5,000 / 105.5%.
c. What would each family member’s average bill be with sales tax?
The average bill with sales tax can be calculated using the same average spending amount from part (a) and adding the tax amount.
Step 1: Calculate the tax amount.
The tax on their bill was 5.5%.
Step 2: Calculate the average bill with sales tax.
The average bill with sales tax would be the average spending amount from part (a) plus the tax amount.
I hope this helps you to understand the process of finding the answers to these questions.