Question

A high school choir is holding a fundraiser for its spring contest tripThe amount each student needs to raise varies as the number of students who participate in the fundraiser. If 50 students participate the fundraiser, each student needs to raise $275
1. The proportional situation represents___variation
2. The constant of variation, k, is equal to___.
3. If all 100 students in choir participate in the fundraiser, each will need to raise___.

Answer 1

Answer:

1. Inverse variation

2. 13750

3. $137.50

Step-by-step explanation:

1. What we have here is an inverse variation

This is because, the total amount that they hope to raise is the same regardless of the number of students

But what will change is the amount to be paid by each student.

In cases where there are higher number of students, the amount to be paid per head will be smaller. While in cases where the number of students are lower, the amount to be paid per head will be higher

So what we have is an inverse variation

2. The constant of variation;

K = SA

where k is the constant , s is the number of students and A is the amount that each will pay

Thus, we have

k = 50 * 275 = $13,750

3. Mathematically, that will be;

Since K = SA

A = K/S

A = 13750/100

A = $137.5

Answer 2

• Part 1:

1. The proportional situation represents inverse variation

• This is because, the total amount that they hope to raise is the same regardless of the number of students

• Part 2:

2. The constant of variation, k, is equal to $13,750.

• K = SA
• k = 50 * 275
• K=$13,750

• Part 3:

3. If all 100 students in choir participate in the fundraiser, each will need to raise $137.5.

K = SA

A = K/S

A = 13750/100

A = $137.5

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