Question

select the correct answer from each drop - down menu.
a high school choir is holding a fundraiser for its spring contest trip. the amount each student needs to raise varies as the number of students who participate in the fundraiser. if 50 students participate in the fundraiser, each student needs to raise $275.
use this information to complete the statements.
this proportional situation represents
the constant of variation, k, is equal to
if all 100 students in choir participate in the fundraiser, each will need to raise

Explanation:

Step1: Identify Variation Type

The amount each student raises ($y$) and the number of students ($x$) have an inverse relationship (more students mean less per student, and vice versa), so it's inverse variation. The formula for inverse variation is $y=\frac{k}{x}$ (or $xy = k$).

Step2: Calculate Constant $k$

Given $x = 50$ and $y = 275$, use $k=xy$.
$k=50\times275 = 13750$

Step3: Find Amount for 100 Students

Now, $x = 100$, $k = 13750$. Use $y=\frac{k}{x}$.
$y=\frac{13750}{100}=137.5$

Answer:

• This proportional situation represents inverse variation.
• The constant of variation, $k$, is equal to $\boldsymbol{13750}$.
• If all 100 students participate, each will need to raise $\boldsymbol{\$137.50}$.