Solve {l}{7=frac{68*9*x+70*9*{(100-x)}}{100}}{y=69}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { 7 = \frac{68 \cdot 9 \cdot x + 70 \cdot 9 \cdot {(100 - x)}}{100} }\\ { y = 69 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$z=69$$

Solution Steps

Consider the first equation. Multiply both sides by 100.

$$7\times 100=68\times 9x+70\times 9\left(100-x\right)$$

Multiply 7 and 100 to get 700.

$$700=68\times 9x+70\times 9\left(100-x\right)$$

Do the multiplications.

$$700=612x+630\left(100-x\right)$$

Use the distributive property to multiply 630 by 100-x.

$$700=612x+63000-630x$$

Combine 612x and -630x to get -18x.

$$700=-18x+63000$$

Swap sides so that all variable terms are on the left hand side.

$$-18x+63000=700$$

Subtract 63000 from both sides.

$$-18x=700-63000$$

Subtract 63000 from 700 to get -62300.

$$-18x=-62300$$

Divide both sides by -18.

$$x=\frac{-62300}{-18}$$

Reduce the fraction \frac{-62300}{-18} to lowest terms by extracting and canceling out -2.

$$x=\frac{31150}{9}$$

The system is now solved.

$$x=\frac{31150}{9} y=69 z=69$$