Write a system of inequalities that represents this situation

Question

Student Government Association decided to do a fundraiser to raise money for a field trip. They decide to sell t-shirts and sweatshirts. The profit for each t-shirt is $10 and the profit for each sweatshirt is $15. The SGA wants to make at least $1000.They want to sell at least 100 items. a. Write a system of inequalities that represents this situation.

Answer 1

Hello Alex!

I think it is important to first assign variables to the objects:

x = T-shirts

y = Sweatshirts

It is also important to look at the language used:

"make at least $1000" - greater than or equal to

"sell at least 100" - greater than or equal to

Since we know that we must sell at least 100 items total:

x + y ≥ 100

We also know that for each T-shirt we sell, we make $10. For each sweatshirt we sell, we make $15. To find an equation that represent this, we must also recall that we must make at least $1000:

($10)x + ($15)y ≥ $1000

Finally, we have our system of equations:

x + y ≥ 100

($10)x + ($15)y ≥ $1000

Answer 2

Choose variables for items for sale

x = t-shirts

y = sweatshirts

System of Inequalities

1^st Inequality

The SGA wants to make at least $1000. (profit goal)

10x + 15y > 1000

2^nd Inequality

They want to sell at least 100 items. (selling goal)

x + y > 100

Answer

10x + 15y > 1000

x + y > 100

Answer 3