A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
(A) 2
(B) 2 1/2
(C) 3
(D) 3 1/2
(E) 4
Answer is B. Let me walk you through.
This is a mixture problem.
Step 1) "A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. "
You should think: 3 parts white, 5 parts black.
That means total there's 8 parts.
More specifically,
3/8 of the mixture is white stuff and 5/8 of the mixture is black stuff.
Step 2) "If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans"
OK. So we know the mixture 2 gallons. How much of these 2 gallons is white stuff and how much of these 2 gallons is black stuff? Of course the white and black stuff must add up to equal 2 gallons.
Well, we know 3/8 of the mixture is white stuff. And the entire mixture is 2 gallons.
So 3/8 of the 2 gallons = 3/8 * 2 = 6/8 = 3/4 = .75 of a gallon is white stuff
Likewise 5/8 of the 2 gallons or 5/8 * 2 = 10/8 = 5/4 = 1.25 of the gallon is black stuff
Step 3) " individual colors can be purchased only in one-gallon or half- gallon cans"
What does this mean? Well, it means that the .75 needs to be rounded up to
1 gallon
And it means the 1.25 gallon needs to be rounded up to
1.5 gallons (a 1 gallon tank and a half gallon tank)
Combine the 1 gallon of white + 1.5 gallon of black = 2.5 total gallons = Answer (B) !!!
Hope that helps!
