Question

A local charity sponsors a 5K race to raise money. It receives $25 per race entry and $5,000 in donations, but it must spend $5 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 more than $25,000. Show your work!

Answer 1

The charity needs at least 1001 entries to raise more than $25000. Let n be the number of race entries, i be the income of the race, and c the cost of the race. The money that the 5K brings in is given by i = 25 * n + 5000 The cost is given by c = n * 5 Now if the charity needs to raise more than 25000 then the income minus the cost must be greater than 25000. 25000 < i - c subsituting for i and c 25000 < i - c = (25 * n + 5000 ) - (5 * n) simplifying results in 25000 < 25*n - 5*n + 5000 25000 < 20*n + 5000 20000 < 20*n 1000 < n The number of entries must be greater than 1000. Since entries must be an integer the charity needs at least 1001 entries.