Solve {l}{frac{16x+12*{(40-x)}}{40}=13}{y=5}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{16 x + 12 \cdot {(40 - x)}}{40} = 13 }\\ { y = 5 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=5$$

Solution Steps

Consider the first equation. Multiply both sides by 40.

$$16x+12\left(40-x\right)=13\times 40$$

Use the distributive property to multiply 12 by 40-x.

$$16x+480-12x=13\times 40$$

Combine 16x and -12x to get 4x.

$$4x+480=13\times 40$$

Multiply 13 and 40 to get 520.

$$4x+480=520$$

Subtract 480 from both sides.

$$4x=520-480$$

Subtract 480 from 520 to get 40.

$$4x=40$$

Divide both sides by 4.

$$x=\frac{40}{4}$$

Divide 40 by 4 to get 10.

$$x=10$$

The system is now solved.

$$x=10 y=5 z=5$$