Question

hints: remember that all the pieces of a pie chart must add up to 100%. it may also help to first write a percent - sentence before solving each problem. on a recent exam, sarahs algebra class received the grade distribution shown in the pie chart to the right. 1. if 10 students scored in the 80 - 89 range on the test, how many students took the exam? 2. what percentage of the class scored a 70 or better? 3. how many students scored at least a 70? algebra exam scores below 50 7.5% 90 and above 22.5% 50 - 59 15% 70 - 79 20%

Explanation:

Step1: Find total number of students

Let the total number of students be $x$. We know that the percentage of students in the 80 - 89 range is $20\%$ (from the pie - chart) and the number of students in this range is 10. We use the formula $\text{Part}=\%\text{ of Total}$, so $10 = 0.2x$.
$x=\frac{10}{0.2}=50$

Step2: Calculate percentage of students scoring 70 or better

The percentage of students scoring 70 or better is the sum of the percentages of students in the 70 - 79, 80 - 89, and 90 and above ranges.
$20\%+20\% + 22.5\%=62.5\%$

Step3: Find number of students scoring at least 70

Since the total number of students $x = 50$ and the percentage of students scoring at least 70 is $62.5\%$, we use the formula $\text{Part}=\%\text{ of Total}$.
Number of students $=0.625\times50 = 31.25\approx31$ (we round down as we are talking about number of students)

Answer:

1. 50 students took the exam.
2. 62.5% of the class scored a 70 or better.
3. 31 students scored at least a 70.