Solve {c}{50+5(t-10)=45+8(t-10)}{x=5t}

$$\left. \begin{array} { c } { 50 + 5 ( t - 10 ) = 45 + 8 ( t - 10 ) } \\ { x = 5 t } \end{array} \right.$$

Solve for t, x

$$x = \frac{175}{3} = 58\frac{1}{3} \approx 58.333333333$$

$$t = \frac{35}{3} = 11\frac{2}{3} \approx 11.666666667$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 5 by t-10.

$$50+5t-50=45+8\left(t-10\right)$$

Subtract 50 from 50 to get 0.

$$5t=45+8\left(t-10\right)$$

Use the distributive property to multiply 8 by t-10.

$$5t=45+8t-80$$

Subtract 80 from 45 to get -35.

$$5t=-35+8t$$

Subtract 8t from both sides.

$$5t-8t=-35$$

Combine 5t and -8t to get -3t.

$$-3t=-35$$

Divide both sides by -3.

$$t=\frac{-35}{-3}$$

Fraction \frac{-35}{-3} can be simplified to \frac{35}{3} by removing the negative sign from both the numerator and the denominator.

$$t=\frac{35}{3}$$

Consider the second equation. Insert the known values of variables into the equation.

$$x=5\times \frac{35}{3}$$

Multiply 5 and \frac{35}{3} to get \frac{175}{3}.

$$x=\frac{175}{3}$$

The system is now solved.

$$t=\frac{35}{3} x=\frac{175}{3}$$