Final answer:
The overall percent change in plan membership at the car wash was a 5% increase, calculated by comparing the total membership increase from 400 to 420 after respective percentage changes of 20% increase for the gold plan and 5% decrease for the silver plan.
Step-by-step explanation:
To determine the overall percent change in plan membership at the car wash, we must first calculate the new memberships for the gold and silver plans after their respective changes.
Initially, there were 160 gold plan members, which increased by 20%.
The increase is 0.20 × 160 = 32, so the new gold plan membership is:
160 + 32 = 192.
The silver plan had 240 members, which decreased by 5%.
The decrease is 0.05 × 240 = 12, so the new silver plan membership is:
240 - 12 = 228.
Next, we calculate the total membership for last month and this month.
Last month's total membership was 160 (gold) + 240 (silver) = 400.
This month's total membership is:
192 (gold) + 228 (silver)
= 420.
The change in quantity is this month's membership minus last month's, which is:
420 - 400 = 20.
Now, we find the percent change using the formula:
Percentage change = (Change in quantity / Quantity) × 100%.
Thus, the percentage change is (20 / 400) × 100%
= 5%.
Hence, the overall plan membership at the car wash increased by 5% to the nearest whole percentage, which means it was a percent increase.