X Nate brought $37.75 to the art supply store he bought a brush a SketchBook and a paint set the brush was 1/4 as much as a SketchBook and the Sketchbook cost 2/3 the cost of the paint set Nate had $2 left over after buying these items.

cost of paint set = $19.5

cost of Sketchbook = $13

cost of brush = $3 ... 25

Step-by-step explanation:

Total money with Nate = $37.75

Let the cost of paint set be $x

As the Sketchbook cost 2/3 the cost of the paint set

Thus cost of Sketchbook = $ (2/3) x

Cost of brush is 1/4 of Sketchbook

Thus cost of brush = (1/4) * (2/3) x = $ 1/6x

Total cost of all the three item in terms of x is

x + (2/3) x + (1/6) x

=> (6x+4x+x) / 6 = 11x/6

Given that after money spent on buying all the three thing Nate has left $2

subtracting money spent on buying three things from total money is equal to $2

Mathematically it can be written as

$37.75 - 11x/6 = $2

=> $37.75 - $2 11x/6

=>$35.75 = 11x/6

=> $35.75*6 = 11 x

=> $214.5 = 11x

=> $214.5/11 = x

=> x = 19.5

Thus,

cost of paint set = x = $19.5

cost of Sketchbook = $ (2/3) x = $ (2/3) * 19.5 = $13

cost of brush = $ 1/6x = $ (1/6) * 19.5 = $3.25