Question

A house painter has 1 gallon of paint that is 35% yellow and another gallon that is 60% yellow. The painter needs a gallon of paint that is 45% yellow. How much of each color should the painter use?

Answer 1

Let $a$ be the volume of the 35% yellow paint the painter will use, and $b$ the volume of the 60% yellow paint.

The painter wants to end up with 1 gal of paint, so

$a+b=1$

Each gallon of 35% yellow paint $a$ contributes 0.35 gal of yellow paint, while each gallon of 60% yellow paint $b$ contributes 0.60 gal of yellow paint. The painter wants to end up with a 45% mixture, so that

$0.35a+0.60b=0.45(a+b)=0.45$

Solve the system and you get

$a=0.6,b=0.4$