Question

#27
susanna collected information about students favorite colors. her results are in the chart.
which statement reflects the information susanna collected?
a for every 4 students who chose red, there are 16 total students.
b for every 2 students who chose green, there are 4 total students.
c for every 10 students who chose purple, there are 2 students who chose green.
d for every 1 student who chose red, there is 4 total students.

Explanation:

Step1: Calculate total number of students

Total students \(=4 + 10+2 + 4=20\)

Step2: Analyze Option A

For red: \(4\) students. Ratio of red - students to total students \(=\frac{4}{20}=\frac{1}{5}\). If we consider the statement “For every 4 students who chose red, there are 16 total students”, ratio \(\frac{4}{16}=\frac{1}{4}
eq\frac{1}{5}\)

Step3: Analyze Option B

For green: \(10\) students. Ratio of green - students to total students \(=\frac{10}{20}=\frac{1}{2}\). If we consider the statement “For every 2 students who chose green, there are 4 total students”, ratio \(\frac{2}{4}=\frac{1}{2}\). But original number of green students is \(10\) and total is \(20\). If we take proportionally, for \(2\) green students (scaled down by factor of \(5\), since \(10\div5 = 2\)), total students should be \(20\div5=4\)

Step4: Analyze Option C

For purple: \(2\) students. Ratio of purple - students to green - students \(=\frac{2}{10}=\frac{1}{5}\). If we consider the statement “For every 10 students who chose purple, there are 2 students who chose green”, ratio \(\frac{10}{2}=5
eq\frac{1}{5}\)

Step5: Analyze Option D

For red: \(4\) students. Ratio of red - students to total students \(=\frac{4}{20}=\frac{1}{5}\). If we consider the statement “For every 1 student who chose red, there is 4 total students”, ratio \(\frac{1}{4}
eq\frac{1}{5}\)

Answer:

B. For every 2 students who chose green, there are 4 total students.