Answer:
The cost of the paintbrush is$3.25, the cost of the sketchbook is $13 and the cost of the paint is $19.50
Step-by-step explanation:
Spencer brought $40.25 to the art supply store and he bought a brush, sketchbook and paint set.
Let the cost of the brush be B.
Let the cost of the sketchbook be S.
Let the cost of the paint set be P.
The cost of the brush was 1/4 as much as a sketchbook. This means that:
[tex]B = \frac{1}{4}S[/tex]___________________(1)
The sketchbook cost 2/3 of the cost of the paint set:
[tex]S = \frac{2}{3}P[/tex]
[tex]=> P = \frac{3}{2}S[/tex]__________________(2)
Spencer had $4.50 left over after buying these items.
This means that the cost of the three materials plus the leftover change will give us $40.25:
[tex]B + S + P + 4.5 = 40.25[/tex]__________(3)
To solve this, let us put (1) and (2) in (3):
[tex]\frac{1}{4}S + S + \frac{3}{2}S + 4.5 = 40.25\\\\=> \frac{1}{4}S + S + \frac{3}{2}S = 40.25 - 4.5\\\\\frac{11}{4}S = 35.75\\ \\S = \frac{35.75 * 4}{11} \\[/tex]
S = $13
Putting the value of S back in (1):
[tex]B = \frac{1}{4} * 13 =[/tex] $3.25
Putting the value of S back in (2):
[tex]P = \frac{3}{2} * 13 =[/tex]$19.50
The cost of the paintbrush is$3.25, the cost of the sketchbook is $13 and the cost of the paint is $19.50.
