Question

In 2012, 34.1% of all glass containers were recycled. A beverage company claims that in 2022, they have increased the recycling rate to 45.6%. What is the percentage increase in the recycling rate?

A. 5.6%

B. 11.5%

C. 34.1%

D. 45.6%

Answer 1

The percentage increase in the recycling rate is found by subtracting the old rate from the new rate, dividing by the old rate, and multiplying by 100. The actual increase in terms of percentage points is 11.5%, which is option B.

Step-by-step explanation:

To calculate the percentage increase in the recycling rate from 2012 to 2022, we will use the percentage increase formula:

Percentage Increase = ((New Value - Old Value) / Old Value) × 100%

Where the New Value is 45.6% and the Old Value is 34.1%. Plugging these values into the formula:

Percentage Increase = ((45.6 - 34.1) / 34.1) × 100% = (11.5 / 34.1) × 100% ≈ 33.72%

This means the rate has increased approximately by 33.72%, but since only 11.5% is the actual difference in percentage points rather than a relative increase percentage, option B is the correct answer.

None of the available answer options correctly reflect the relative percentage increase calculated, but B reflects the change in percentage points.

To find the percentage increase in the recycling rate, you subtract the initial rate from the final rate and divide by the initial rate. In this case, the initial rate is 34.1% and the final rate is 45.6%. So, the percentage increase is calculated as (45.6 - 34.1) / 34.1 = 0.336 = 33.6%.

Therefore, the correct answer is C. 34.1%.