Question

A car wash offers its customers two plans: a gold plan and a silver plan.
• Last month, 160 customers had the gold plan and 240 customers had the silver plan.
• This month, membership for the gold plan increased by 20% and membership for the silver plan decreased by 5% compared to last month.
Part A
To the nearest whole percentage, what was the overall percent change in plan membership at the car wash? Enter the answer in the box.
%
Part B
Was the overall change a percent decrease or a percent increase?
A. percent decrease
B. percent increase

Answer 1

To solve the problem, we will follow these steps:


### Part A: Overall Percent Change in Plan Membership

1. **Calculate the total number of customers last month:**
- Gold plan customers last month = 160
- Silver plan customers last month = 240

\[
\text{Total last month} = 160 + 240 = 400
\]

2. **Calculate the number of customers this month for each plan:**
- Gold plan customers this month:
- Increase by 20% means \( 160 \times 1.20 = 192 \)

- Silver plan customers this month:
- Decrease by 5% means \( 240 \times (1 - 0.05) = 240 \times 0.95 = 228 \)

3. **Calculate total number of customers this month:**
\[
\text{Total this month} = 192 + 228 = 420
\]

4. **Calculate the overall percent change in membership:**
\[
\text{Percent Change} = \left( \frac{\text{Total this month} - \text{Total last month}}{\text{Total last month}} \right) \times 100
\]
\[
\text{Percent Change} = \left( \frac{420 - 400}{400} \right) \times 100 = \left( \frac{20}{400} \right) \times 100 = 5\%
\]

So, the overall percent change in plan membership is **5%**.


### Part B: Type of Change

Since the overall percent change is positive (5%), the change is classified as an increase.

Thus, the answer is:

B. percent increase