QuestionAre the ratios of canned goods per student the same for Mr. Alvarez, Ms. Jensen, and Mrs. Saunders? Show your work.

Studdy Solution

STEP 1

Assumptions1. The number of students and goods collected in Mr. Alvarez's homeroom are25 and150 respectively. . The number of students and goods collected in Ms. Jensen's homeroom are28 and154 respectively.
3. The number of students and goods collected in Mrs. Saunders's homeroom are27 and162 respectively.
4. The ratio of canned goods per student is calculated by dividing the number of goods collected by the number of students.

STEP 2

First, we need to find the ratio of canned goods per student in each homeroom. We can do this by dividing the number of goods collected by the number of students.
For Mr. Alvarez's homeroom, the ratio is $\text{Ratio}_{\text{Alvarez}} = \frac{\text{Goods Collected}}{\text{Number of Students}}$

STEP 3

Now, plug in the given values for the number of goods collected and the number of students in Mr. Alvarez's homeroom to calculate the ratio.
$\text{Ratio}_{\text{Alvarez}} = \frac{150}{25}$

STEP 4

Calculate the ratio of canned goods per student in Mr. Alvarez's homeroom.
$\text{Ratio}_{\text{Alvarez}} = \frac{150}{25} =6$

STEP 5

Repeat the same process for Ms. Jensen's and Mrs. Saunders's homerooms.
For Ms. Jensen's homeroom, the ratio is $\text{Ratio}_{\text{Jensen}} = \frac{\text{Goods Collected}}{\text{Number of Students}} = \frac{154}{28}$ For Mrs. Saunders's homeroom, the ratio is $\text{Ratio}_{\text{Saunders}} = \frac{\text{Goods Collected}}{\text{Number of Students}} = \frac{162}{27}$

STEP 6

Calculate the ratio of canned goods per student in Ms. Jensen's and Mrs. Saunders's homerooms.
$\text{Ratio}_{\text{Jensen}} = \frac{154}{28} \approx5.5$ $\text{Ratio}_{\text{Saunders}} = \frac{162}{27} =6$

STEP 7

Now that we have the ratios for each homeroom, we can compare them to see if they are equivalent.
The ratios areMr. Alvarez's homeroom6Ms. Jensen's homeroom5.5Mrs. Saunders's homeroom6From these values, we can see that the ratios of canned goods per student are not equivalent in all the homerooms. The ratio in Ms. Jensen's homeroom is different from the ratios in Mr. Alvarez's and Mrs. Saunders's homerooms. However, the ratios in Mr. Alvarez's and Mrs. Saunders's homerooms are equivalent.

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