Question

Determine whether the statement makes sense or does not make sense, and explain your reasoning. "My weight increased by 4% in January and 4% in February, so my increase in weight over the two months is 8%." Choose the correct answer below.

A. The statement does not make sense because the actual percent increase is 8.16%.
B. The statement does not make sense because the actual percent increase is 16%.
C. The statement makes sense because 4% plus 4% is 8%.
D. The statement makes sense because 4% times 4% divided by 2% is 8%.

Answer 1

The statement given by the student is incorrect because percentage increases are multiplicative rather than additive. The actual weight increase over two months is 8.16%, which demonstrates the need to apply percentages to the updated amount sequentially. Option A is the correct answer.

Step-by-step explanation:

The statement "My weight increased by 4% in January and 4% in February, so my increase in weight over the two months is 8%" does not quite make mathematical sense because percent increases on sequential changes are multiplicative, not additive.

To illustrate this, if a student's initial weight is W, after a 4% increase in January, their weight becomes W + 0.04W = 1.04W. Then a further 4% increase in February would be applied to the new weight, giving 1.04W + 0.04(1.04W) = 1.04W + 0.0416W = 1.0816W.

Therefore, the total percent increase over the two months is 1.0816W - W, which is 0.0816W, or 8.16% of the original weight, not 8%. This demonstrates a common misconception that the same percentage increase over different time periods can simply be added together.

The correct answer is A. The statement does not make sense because the actual percent increase is 8.16%, not 8%.