Question

A painter has 10 gallons of orange paint that is 50% red paint and
50% yellow paint. How many gallons of red and yellow paint could
this painter add to make orange paint that is 60% red paint and 40%
yellow paint?

Answer 1

Let's first calculate the current amounts of red and yellow paint in the 10 gallons of orange paint.

Red paint = 10 gallons * 50% = 5 gallons
Yellow paint = 10 gallons * 50% = 5 gallons

Let x be the amount of red paint added and y be the amount of yellow paint added.

The total volume of paint after adding red and yellow paint = 10 gallons + x + y

The percentage of red paint after adding the new paint = (5 gallons + x) / (10 gallons + x + y)
The percentage of yellow paint after adding the new paint = (5 gallons + y) / (10 gallons + x + y)

We want to create a mixture that is 60% red paint and 40% yellow paint:

(5 gallons + x) / (10 gallons + x + y) = 60%
(5 gallons + y) / (10 gallons + x + y) = 40%

Solving these two equations simultaneously gives us:

x = 5
y = 5

Therefore, the painter would need to add 5 gallons of red paint and 5 gallons of yellow paint to create the desired mixture.