Geometry Word Problem

Question

As a part of her interior design job, Isabel has been tasked with painting two walls of a customer's dining room. In order to maximize her profit from the job, she wishes to minimize the materials cost for the job. The paint the customer insists upon comes in right cylindrical containers and can be purchased only for either $5 per quart or $8 per gallon. A one gallon container of the particular paint covers 200 square feet. The two walls of the dining room she needs to paint are both 8 feet high and 16 feet long. How much paint should she purchase in order to cover the two walls for the lowest cost? 

 

A) She should buy one gallon of paint

 

B) She should buy two gallons of paint

 

C) She should buy one gallon and one quart of paint

 

D) She should buy one gallon and two quarts of paint

Answer 1

First, lets figure out how many square feet of wall Isabel has to paint. She'll paint two walls, each 8 feet by 16 feet. The formula for area is:

 

Area = length × width

 

In your case, let length = 16 and width = 8. Then:

 

Area = 16(8) = 128

 

Since there are two walls, Isabel needs to paint 128(2) = 256 square feet.

 

 

The problem tells you that the gallon paint can covers 200 square feet. A quart is 1/4 of a gallon, so the quart paint can will cover 200(1/4) = 50 square feet. The gallons are definitely more cost-effective, since four quarts have the same amount of paint as a gallon but cost $5(4) = $20 instead of $8. So Isabel will definitely want to buy one gallon can to cover 200 of the 256 square feet.

 

What about the remaining 56 square feet? That would take two quart cans (100 square feet) or one gallon can (200 square feet) to cover. Either option will work; Isabel just wants to find the cheapest. Two quart cans cost $5(2) = $10 while one gallon can costs $8. So it's actually cheaper to buy another gallon can to cover the remaining 56 square feet.

 

 

That means option B is correct: she should buy two gallons of paint.

Answer 2

First find the area of the two walls that need to be painted by using the formula Area= L x W

 

Both of the walls are 8 ft high(L) and 16 ft long(W)

 

Area = 8 x 19 = 128 ft² 

 

There are two walls so we need to double that number to 256 ft² 

 

• 1 gallon can covers 200 square feet, that would leave 56 square feet to be painted

 

• It is important to understand that 4 quarts equals 1 gallon

 

• If 1 gallon covers 200 square feet, that means half a gallon will cover 100 square feet. Half a gallon is equal to 2 quarts

 

Therefore, D) Isabla should buy 1 gallon and 2 quarts of paint.