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Cara brought $34.50 to the art supply store. she bought a brush, a sketchbook, and a paint set. the brush was 1 3 as much as the sketchbook, and the sketchbook cost 1 2 the cost of the paint set. cara had $2.00 left over after buying these items.

Respuesta :

Using a system of equations, it is found that the cost of a paint set is of $19.50.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

  • Variable x: cost of a paint set.
  • Variable y: cost of a sketchbook.
  • Variable z: cost of a brush.

Cara brought $34.50 to the art supply store, bought one of each item, and had $2.00 left, hence:

x + y + z = 32.50.

The sketchbook cost half the cost of the paint set, hence:

y = 0.5x.

The brush cost one third of the sketchbook, hence:

z = 0.3333(0.5x) = 0.1667x.

Then, to solve for x:

x + y + z = 32.50

x + 0.5x + 0.1667x = 32.50

x = 32.50/1.6667

x = 19.50.

The cost of a paint set is of $19.50.

More can be learned about a system of equations at https://brainly.com/question/24342899

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