Question

Plz help me!

She found that one gallon of paint will cover an area of no more than 400 square feet. If she only has half of a gallon of paint left, write an inequality that could be used to find the maximum height, in feet, of each stripe. Then, determine if the given stripe height would be viable for this situation.

Answer 1

Area of the three equally sized stripes: A

A=(x+15)(x)(3)
A=3x(x+15)
A=3x^2+45x

One gallon of paint will cover an area of no more than 400 square feet: <=400

She only has half of a gallon of paint left:
1/2(400 square feet)=400/2=200 square feet

Inequality that could be used to find the maximum height, in feet, of each stripe:
A<=200
3x^2+45x<=200

Answer: 3x^2+45x <= 200

Could her stripes be 3' tall?
x=3→A=3(3)^2+45(3)=3(9)+135=27+135→A=162<200 Ok
Yes, her stripes could be 3' tall.
Answer: Yes

Could her stripes be 4' tall?
x=4→A=3(4)^2+45(4)=3(16)+180=48+180→A=228>200 No
No, her stripes couldn't be 4' tall.
Answer: No