Question

hana’s math grade increased from 65 to 86. fiona’s math grade increased from 70 to 80. what is the difference, rounded to the nearest whole number, between the approximate percent increases?
10 percent
15 percent
18 percent
21 percent

Explanation:

Step1: Calculate Ilana's percent increase

First, find the increase in Ilana's grade: \( 86 - 65 = 21 \). Then, use the percent increase formula \( \text{Percent Increase} = \frac{\text{Increase}}{\text{Original}} \times 100\% \). So, \( \frac{21}{65} \times 100\% \approx 32.31\% \)? Wait, no, wait the problem is about the difference between Ilana's and Fiona's percent increases. Wait, let's re - read.

Wait, Ilana's grade: from 65 to 86. Fiona's grade: from 70 to 80.

First, calculate Ilana's percent increase:

Increase for Ilana: \( 86 - 65 = 21 \)

Percent increase for Ilana: \( \frac{21}{65} \times 100\% \approx \frac{21}{65}\times100\approx 32.31\% \)? No, that can't be. Wait, maybe I misread. Wait the question is: "Ilana’s math grade increased from 65 to 86. Fiona’s math grade increased from 70 to 80. What is the difference, rounded to the nearest whole number, between the approximate percent increases?"

Oh! I see. So first, calculate Ilana's percent increase and Fiona's percent increase, then find the difference.

Step1: Calculate Ilana's percent increase

Increase for Ilana: \( 86 - 65 = 21 \)

Percent increase formula: \( \text{Percent Increase} = \frac{\text{New - Old}}{\text{Old}} \times 100\% \)

For Ilana: \( \frac{86 - 65}{65} \times 100\%=\frac{21}{65}\times 100\% \approx 32.31\% \)

Step2: Calculate Fiona's percent increase

Increase for Fiona: \( 80 - 70 = 10 \)

Percent increase for Fiona: \( \frac{80 - 70}{70} \times 100\%=\frac{10}{70}\times 100\% \approx 14.29\% \)

Step3: Find the difference between the two percent increases

Difference: \( 32.31\% - 14.29\% \approx 18.02\% \), which rounds to 18 percent.

Wait, but the options are 10, 15, 18, 21. So the difference is approximately 18 percent.

Wait, let's recalculate Ilana's percent increase:

\( \frac{86 - 65}{65}=\frac{21}{65}\approx0.323 \), times 100 is 32.3%

Fiona's: \( \frac{80 - 70}{70}=\frac{10}{70}\approx0.1429 \), times 100 is 14.29%

Difference: \( 32.3 - 14.29 = 18.01\approx18 \)

Answer:

18 percent (corresponding to the option "18 percent")