In Kendra’s class, 40 percent of the students earned an A on the math test. Twenty students earned an A. Kendra needs to find out how many students are in her class. Kendra’s work is shown below.

Question

StartFraction part Over whole EndFraction = StartFraction 40 divided by 2 Over 100 times 2 EndFraction = StartFraction 20 Over 200 EndFraction

What mistake did Kendra make?
Kendra should have multiplied by 4 in both the numerator and the denominator.
Kendra should have divided by 2 instead of multiplying by 2 in the denominator.
Kendra should have added 40 and 20.
Kendra should have the part to whole equation written as StartFraction 100 Over 40 EndFraction.

Answer 1

Kendra's mistake lies in how she set up her equation. The correct approach should have recognized that 40 percent corresponds to 20 students in Kendra's class.

The equation represents the relationship between the part (students earning an A) and the whole (total students). Kendra indicates:

\[ \text{part (students with an A)} = 20 \] \[ \text{percent} = 40% \]

To find the whole number of students (let's call it \(x\)), we can set up the equation based on percentages:

\[ \frac{20}{x} = \frac{40}{100} \]

Now, if we cross-multiply, we get:

\[ 20 \cdot 100 = 40 \cdot x \] \[ 2000 = 40x \] \[ x = \frac{2000}{40} = 50 \]

So, the total number of students in Kendra's class is 50.

Looking at Kendra's work, she mistakenly multiplied by 2 instead of appropriately setting up and solving the proportion. Therefore, the correct answer regarding her mistake is:

Kendra should have divided by 2 instead of multiplying by 2 in the denominator.