Question

The Leukemia and Lymphoma Society 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

(I have no idea how to do this. It's just extra credit but I need it)

Answer 1

The net amount they raise is the amount they receive minus what they pay in expenses.

They receive:
$10,000 fixed amount in donations
$55 per person

They pay:
$15 per person

If there are x number of entries, they receive 55x from the entries.
Also, they pay 15x for the entries.

The net amount they raise is amount they receive min us amount they pay:

55x + 10,000 - 15x

which simplifies to

40x + 10,0000

They want to raise at least $55,000.
At least $55,000 means $55,000 or more.
They want to raise an amount greater than or equal to $55,000.

Now we write the inequality:

40x + 10,000 >= 55,000

Now we solve the inequality for x, the number of entries.

40x >= 45,000

x >= 1125

They must have 1125 or more race entries to raise $55,000.