Question

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) 2.5(C) 3(D) 3.5(E) 4

Answer 1

3 parts whiite with 5 parts black = 8 parts in total

So, fractional white is:

`(3)/(8)`

and, fractional black is:

`(5)/(8)`

For 2 gallons, we need:

`\begin{gathered} 2\cdot(3)/(8)=(6)/(8)=(3)/(4)=0.75\text{ gallons white} \\ \text{and} \\ 2\cdot(5)/(8)=(10)/(8)=(5)/(4)=1.25\text{ gallons black} \end{gathered}`

Remember, we can buy only 1 gallons and half gallon cans.

Thus,

• 0.75 gallons of white paint needed will be acquired from 1 gallon can.

,

• To get 1.25 gallons of black paint, we would need one 1 gallon can and one half-gallon can. Total of 1.5 gallons.

Thus, we need 1 + 1.5 = 2.5 gallons.

Correct Answer

B