Question

your club awards one student a $2000 scholarship, and each member contributes an equal amount. Your contribution y depends on the number of members x. Write an inverse variation equation that represents this situation

Answer 1

The inverse variation equation that represents this situation is:

xy = k

where x is the number of members, y is the contribution made by each member, and k is a constant of proportionality.

Since each member contributes an equal amount, we can let y be the contribution made by each member. If there are x members, then the total amount contributed is 2000 + xy. Since this total amount is divided equally among the x members, we can set y equal to the total amount divided by x, which gives:

y = (2000 + xy) / x

Multiplying both sides by x, we get:

xy = 2000 + xy

Subtracting xy from both sides, we get:

0 = 2000

This is a contradiction, which means that our assumption that y depends on x is incorrect. Therefore, we cannot write an inverse variation equation that represents this situation.

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