Problem Solving

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

Thank you for your help

It will be 1 and 1/2 gallons of Black Paint and 1 gallon of white paint.
This will be 5 part of the mixture. We will use more than 1 gallon as more Black paint is needed but < 2 gallon. Total mixture is 2 gallons.
Of the 1 gallon white paint more than 1/2 gallon will be used.
1/2 tin is not sufficient. Since we have to use more 1/4 or 3 parts of the total mixture.

SO we need 2.5 gallons

Sorry but it is not clear for me.
Could you re explain with an equation.
Thank you

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!

@ gmatpll , it was a cakewalk
&
Welcome to the forum.