Question

there are 75 seventh grade students and 50 eighth grade students going on a field trip. the teachers want to split the students into as many groups as possible that have the same number of seventh and eighth grade students in each.

which of the following statements are true about the groups the students will be split into?

select all that apply.

a there will be 25 groups.
b there will be 5 groups.
c there will be 3 seventh graders per group.
d there will be 10 eighth graders per group.
e there will be 5 seventh graders per group.

Explanation:

Identify the given values and goal

Using the Word Problems knowledge point

• Seventh graders: \(75\)
• Eighth graders: \(50\)
• Goal: Split into as many groups as possible with the same number of seventh and eighth graders in each.

Find the greatest common factor

Using the Greatest Common Factor knowledge point

$$
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$$

Calculate students per group

Using the Word Problems knowledge point

• Number of groups: \(25\)
• Seventh graders per group: \(\frac{75}{25} = 3\)
• Eighth graders per group: \(\frac{50}{25} = 2\)

Evaluate the given statements

Using the Word Problems knowledge point

• Statement A: "There will be 25 groups" is true.
• Statement B: "There will be 5 groups" is false.
• Statement C: "There will be 3 seventh graders per group" is true.
• Statement D: "There will be 10 eighth graders per group" is false.
• Statement E: "There will be 5 seventh graders per group" is false.

Answer:

• **(A) There will be 25 groups.</mcq-option>
• (B) There will be 5 groups.

<mcq-correct>(C) There will be 3 seventh graders per group. (Correct answer)**

• (D) There will be 10 eighth graders per group.
• (E) There will be 5 seventh graders per group.