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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?

Respuesta :

LammettHash

Let [tex]a[/tex] be the volume of the 35% yellow paint the painter will use, and [tex]b[/tex] the volume of the 60% yellow paint.

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

[tex]a+b=1[/tex]

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

[tex]0.35a+0.60b=0.45(a+b)=0.45[/tex]

Solve the system and you get

[tex]a=0.6,b=0.4[/tex]