Question

2.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

We know that it receives $55 per race entry, but it must spend $15 per race entry to cover the cost of the race.

`\text{ \$55-\$15=\$40}`

So, it really receives $40 per race entry.

We also know that it receives $10,000 in donations.

If the charity needs to raise at least $55,000, to find the number of race entries that it needs we can use the next inequality

`40x+10000\ge55000`

Where, x represents the number of race

Finally, we must solve the inequality

`\begin{gathered} 40x\ge55000-10000 \\ x\ge1125 \end{gathered}`

So, the charity needs 1125 race entries to raise at least $55000