Question

A random survey was conducted about students’ favorite vegetables. Ten students voted for green beans, 12 students voted for corn, and 3 students voted for broccoli. Rachel concludes that 240 of the 600 students in the school are expected to prefer green beans. Is her conclusion valid? Explain.

Answer 1

Answer:

Rachel's conclusion is valid. The ratios for green beans to total students for the survey and the school form a proportion.

Step-by-step explanation:

Solve using proportions. The format should be "Green beans" on the top, and "Total students" on the bottom.

$\frac{survey:green.beans}{survey:total} =\frac{school:green.beans}{school:total}$

$\frac{10}{10+12+3} =\frac{240}{600}$    Simplify the first numerator

$\frac{10}{25} =\frac{240}{600}$      Find the common ratio

The common ratio is the number you multiply by to get from the top left to top right. It's the same number the you can multiply the bottom left number by to get the bottom right.

Divide the right side by the left side to find the ratio.

Top: ratio = 240/10 = 24

Bottom: ratio = 600/25 = 24

Since the ratios are the same, they are common.

Therefore the proportion is correct, and Rachel's conclusion is valid.