Question

A local charity sponsors a 5K race to raise money. It receives $55 per race entry and $10,000 in donations, but it must spend $15 per race entry to cover the cost of the race.

Write and solve an inequality to determine the number of race entries the charity needs to raise at least $55,000.


Answer:

Answer 1

Answer: At least 1125 race entries

In other words, there needs to be 1125 or more entries

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Work Shown:

x = number of race entries

The charity gets $55 per race entry

1 entry = 55 dollars donated

x entries = 55x dollars donated

This is ignoring the fact that "it must spend $15 per race entry to cover the cost of the race."

If we include this cost, then they're really pulling in 55-15 = 40 dollars per entry.

So we have to update the 55x into 40x

Add this onto the 10,000 in donations they get elsewhere

We have the expression 40x+10,000

We want this to be at least 55,000

So we want 40x+10,000 to be 55,000 or larger

We can say the following

`40x + 10,000 \ge 55,000\\\\40x \ge 55,000 - 10,000\\\\40x \ge 45,000\\\\x \ge 45,000 / 40\\\\x \ge 1,125\\\\`

This means there needs to be at least 1125 race entries.