Question

A booth at the circus is taking donations for the children's hospital. They noticed on Saturday that more than 217 people donated money. Women averaged a donation of $18, and men averaged a donation of $16. Which system of inequalities could be used to determine the number of women (w) and men (m) who donated, if no more than $3,702 was donated?

Answer 1

Explanation:

Let M be the number of men donors and W the number of women donors.

We are told that M + W => 217 {"They noticed on Saturday that more than 217 people donated money."]

The total donations of no more than $3,702 consists of Men: ($16)M and Women: ($18)W

This makes the following equation:

18W + 16M <= 3702 ["no more than $3,702 was donated"]

The two equations are:

18W + 16M <= 3702, and

M + W => 217

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Extra credit:

To find the number of men and women donors, let's assume the equations are correct without the inequality signs.

Rearrange:

M + W => 217

M = 217-W

Now use this definition of M in the second equation:

18W + 16(217-W) = 3702

'

Solve for W: W = 115: There were 115 women donors at $18 each: $207.

That means 217 - 115 or 102 men at $16 each: &1632

Total donations of $3702