Answer:
• The proportional situation represents an Inverse Variation
,
• The constant of variation, k = 13750
,
• If all 100 students participate in the fundraiser, each will contribute $137.5
Explanation:
From the given information, we notice that the more students involved in the fundraiser, the less the amount each student needs to contribute.
This is an INVERSE VARIATION
Let s represent the number of students who participated in the fundraiser, and t represents the amount needed to be contributed by each student, we have:
[tex]\begin{gathered} s\propto\frac{1}{t} \\ \\ \Rightarrow s=\frac{k}{t} \\ \\ OR \\ st=k \end{gathered}[/tex]
To find k, we use the information that s = 50 when t = 275
So,
[tex]\begin{gathered} k=50\times275 \\ =13750 \end{gathered}[/tex]
From the above, we have the formula:
[tex]st=13750[/tex]
If 100 students participate in the fundraiser, we have:
[tex]\begin{gathered} 100t=13750 \\ t=\frac{13750}{100}=137.5 \end{gathered}[/tex]
Each student needs to contribute $137.5
