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In order to make a specific shade of green paint, a painter mixes 1/2
of a gallon of blue paint with 4/5 of a gallon of yellow paint.Write an equation to represent the number of gallons of yellow paint, y needed for any amount of blue paint, b.

PLEASE include the constant of constant of proportionality

Answer :

The proportional equation for the the number of gallons of yellow paint, y needed for any amount of blue paint, b is:

  • [tex]y(b) = \frac{8}{5}b[/tex]

Proportional equation:

  • A proportional equation is modeled by:

[tex]y(b) = ab[/tex]

  • In which a is the constant of proportionality.

In this problem, the parameters are:

  • [tex]\frac{1}{2}[/tex] of a gallon of blue paint, hence [tex]b = \frac{1}{2}[/tex]
  • [tex]\frac{4}{5}[/tex] of a gallon of yellow paint, hence [tex]y = \frac{4}{5}[/tex].

Then, to find the constant of proportionality:

[tex]y(b) = ab[/tex]

[tex]\frac{4}{5} = \frac{1}{2}a[/tex]

[tex]a = \frac{8}{5}[/tex]

Hence, the equation is:

[tex]y(b) = \frac{8}{5}b[/tex]

You can learn more about proportional equation at https://brainly.com/question/13112448

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