Question

Mateo spent a total of \(36 on 10 art supply items. How many bottles of paint and paint brushes did Mateo buy?

Acrylic Paint - \)5

Paint Brushes - $1.50

Short answer

The number of bottles of paint and the number of paint brushes bought by Mateo are 6 and 4 respectively.

Step-by-step solution

Step 1. State the concept of elimination method.

The elimination method is the method in which addition or subtraction method is used to get an equation in the one variable.

If the coefficients are opposite, use the addition and when the coefficients are same, use the subtraction.

Step 2. Add or subtract the equations to eliminate one variable. 

Let the number of bottles of paint bought be x and the number of paint brushes bought be y.

As per the conditions the system of equations thus formed will be:

$x+y=10$ … (1)

$5x+1.50y=36$ … (2)

Multiply equation (1) by 5.

$$\begin{gathered} 5\left(x+y\right)=5\times \left(10\right) \\ 5x+5y=50\left(3\right) \end{gathered}$$

Note that both the equations (2) and (3) have $5x$in same sign, therefore, variable $x$can be eliminated if both equations are subtracted.

$\begin{array}{l}5x+5y=50\\ \underset{¯}{\left(-\right)5x+1.50y=36}\\ 3.5y=14\text{Dividebothsidesby3.5}\\ y=4\end{array}$

Step 3. Solve for x.

Substitute 4 for y into the equation (1) and solve for x.

$\begin{array}{c}x+y=10\\ x+\left(4\right)-4=10-4\\ x=6\end{array}$

Therefore, the number of bottles of paint and the number of paint brushes bought are 6 and 4 respectively.