Question

20 POINTS PLEASE HELP!!!!!!! The Children’s Hospital sponsors a 10K race to raise money. It receives $75 per race entry and $10,000 in donations, but it must spend $25 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 $100,000.

Answer 1

The number of race entries must be at least 1800.

Explanation:

Suppose, the number of race entries is
`x`

It receives $75 per race entry. So, the total amount received from the race entries
`=\$75x`

It also receives $10000 in donations. So, the total amount received
`=(75x+10000) dollar`

Now, it must spend $25 per race entry to cover the cost of the race. So, the total amount spend for all race entries
`= \$25x`

Given that, the charity needs to raise at least $100,000. So, the inequality will be........

`(75x+10000)-25x\geq 100000\\ \\ 50x+10000\geq 100000\\ \\ 50x\geq 90000\\ \\ x\geq (90000)/(50) \\ \\ x\geq 1800`

So, the number of race entries must be at least 1800.