A painter needs to have 24 gallons of paint that contains 30% solvent how many gallons of paint contain 20% solvent and how many gallons containing 60% solvent?

18 gallons containing 20% solvent and 6 gallons containing 60% solvent

Step-by-step explanation:

the painter needs 24 gallons of paint containing 30% solvent = 7.2 gallons of solvent

let a = 20% solvent paint

let b = 60% solvent paint

a + b = 24

0.2a + 0.6b = 7.2

(replace a = 24 - b in the second equation)

a + b = 24

0.2 (24 - b) + 0.6b = 7.2

4.8 - 0.2b + 0.6b = 7.2

0.4b = 7.2 - 4.8 = 2.4

b = 2.4 / 0.4 = 6

a = 24 - 6 = 18