Solve {l}{a+t=8000}{0.10+0.12t=900}

$$\left. \begin{array} { l } { a + t = 8000 } \\ { 0.10 + 0.12 t = 900 } \end{array} \right.$$

Solve for a, t

$$t = \frac{44995}{6} = 7499\frac{1}{6} \approx 7499.166666667$$

$$a = \frac{3005}{6} = 500\frac{5}{6} \approx 500.833333333$$

Solution Steps

Consider the second equation. Subtract 0.1 from both sides.

$$0.12t=900-0.1$$

Subtract 0.1 from 900 to get 899.9.

$$0.12t=899.9$$

Divide both sides by 0.12.

$$t=\frac{899.9}{0.12}$$

Expand \frac{899.9}{0.12} by multiplying both numerator and the denominator by 100.

$$t=\frac{89990}{12}$$

Reduce the fraction \frac{89990}{12} to lowest terms by extracting and canceling out 2.

$$t=\frac{44995}{6}$$

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

$$a+\frac{44995}{6}=8000$$

Subtract \frac{44995}{6} from both sides.

$$a=8000-\frac{44995}{6}$$

Subtract \frac{44995}{6} from 8000 to get \frac{3005}{6}.

$$a=\frac{3005}{6}$$

The system is now solved.

$$a=\frac{3005}{6} t=\frac{44995}{6}$$