Chapter 5, Problem 7CR

To determine

To find:The number of brushes and tubes of paint purchased.

Answer to Problem 7CR

8 brushes and 4 tubes of paint were purchased.

Explanation of Solution

Given information:Atotal of $20 was spent on tubes of paint and brushes for an art project. Tubes of paint cost $4.00 each and paintbrushes cost $0.50 each. There are twice as many brushes as tubes of paint.

Calculation:Let the number of tubes of paint be x and that of paintbrushes be y .

Each tube of paint costs $4.00.

Then x tubes of paint cost $\$4.00x$

Each paintbrush costs $0.50.

Then y paintbrushes cost $\$0.50y$

So, total cost $=4.00x+0.50y$

Total cost of the tubes and paint and paintbrushes is $20 and there are twice as many brushes as tubes of paint.

Then, by the problem,

  $\begin{array}{l}4.00x+0.50y=\mathrm{20.................}(1)\\ y=2x\mathrm{.................}(2)\end{array}$

Substituting equation (2) in (1),

  $\begin{array}{l}4.00x+0.50y=20\\ \Rightarrow 4.00x+0.50(2x)=20\\ \Rightarrow 4.00x+1.00x=20\\ \Rightarrow 5.00x=20\\ \Rightarrow x=4\end{array}$

Putting $x=4$ in equation (2),

  $\begin{array}{l}y=2x\\ \Rightarrow y=2\times 4\\ \Rightarrow y=8\end{array}$

Then, the solution is

  $\begin{array}{l}x=4\\ y=8\end{array}$

Thus, 8 brushes and 4 tubes of paint were purchased.