Question

The school athletics department is raising money for new gym equipment. To raise $7,200 by spring training, the department decides to sell T-shirts during the fall semester. Based on previous fundraising drives, the expression

–
10p+560 can be used to gauge how many shirts the department will sell depending on the price of a shirt, p.
What is the lowest shirt price the athletics department can use to raise exactly $7,200 in revenue?

Answer 1

The expression given, -10p+560, represents the revenue generated by selling T-shirts, based on the price of a shirt, p. To determine the lowest shirt price the athletics department can use to raise exactly $7,200 in revenue, we can set the expression equal to $7,200 and solve for p.

-10p+560 = 7200

Subtracting 560 from both sides:

-10p = 6640

Dividing both sides by -10:

p = -664

This answer does not make sense as a price for a T-shirt. The negative value suggests that the expression does not apply for such a low price. Therefore, we can assume that the athletics department cannot sell T-shirts at such a low price.

To find the lowest possible price for a T-shirt that will raise exactly $7,200, we need to find the value of p that makes the expression equal to 7,200.

-10p+560 = 7200

Subtracting 560 from both sides:

-10p = 6640

Dividing both sides by -10:

p = -664

Again, this answer does not make sense.

Therefore, we need to try a higher price for the T-shirt. Let's try a price of $20 per shirt:

-10(20)+560 = 360

This means that for every T-shirt sold at $20, the revenue generated will be $360.

To find out how many T-shirts need to be sold to raise $7,200, we can set up an equation:

360x = 7200

Dividing both sides by 360:

x = 20

This means that the athletics department will need to sell 20 T-shirts at $20 each to raise exactly $7,200 in revenue.