Question

An animal shelter conducts an annual fundraising drive. The animal shelter must raise at least enough money to cover their annual rental of $2,500 and weekly expenses of $450. So far, the shelter has received a one-time donation of $125 and pledged donations of $680 per week. Write an inequality for the situation and solve for w, the number of weeks it can take the shelter to meet the goal? (Round to the nearest tenth.)

Answer 1

The minimum number of weeks the animal shelter needs to receive donations to meet their funding goal is at least 10.3 weeks. This is determined by setting up an inequality with the shelter's expenses and donations, then solving for the number of weeks, w.

Step-by-step explanation:

We need to write an inequality for the animal shelter's fundraising situation to determine the minimum number of weeks, w, they must receive donations to meet their goal. They start with a one-time donation of $125, their annual rental cost is $2,500, and they have weekly expenses of $450. They receive $680 per week in pledged donations. The inequality will compare their total earnings from pledges over a number of weeks to their total necessary expenses over the same period.

The inequality looks like this:

680w + 125 ≥ 450w + 2,500

Solving for w gives:

230w ≥ 2,375
w ≥ ≈ 10.3 weeks

The animal shelter needs to receive donations for at least 10.3 weeks to meet their funding goal, rounding to the nearest tenth.