Solve 100-99/99-81=frac{100-{t}_{0}}{{t}_{0}-83}

$$\frac{ 100-99 }{ 99-81 } = \frac{ 100- { t }_{ 0 } }{ { t }_{ 0 } -83 }$$

Solve for t_0

$$t_{0} = \frac{1883}{19} = 99\frac{2}{19} \approx 99.105263158$$

Steps for Solving Linear Equation

Variable t_{0} cannot be equal to 83 since division by zero is not defined. Multiply both sides of the equation by t_{0}-83.

$$\left(\frac{1}{18}t_{0}-\frac{83}{18}\right)\left(100-99\right)=100-t_{0}$$

Subtract 99 from 100 to get 1.

$$\left(\frac{1}{18}t_{0}-\frac{83}{18}\right)\times 1=100-t_{0}$$

Use the distributive property to multiply \frac{1}{18}t_{0}-\frac{83}{18} by 1.

$$\frac{1}{18}t_{0}-\frac{83}{18}=100-t_{0}$$

Add t_{0} to both sides.

$$\frac{1}{18}t_{0}-\frac{83}{18}+t_{0}=100$$

Combine \frac{1}{18}t_{0} and t_{0} to get \frac{19}{18}t_{0}.

$$\frac{19}{18}t_{0}-\frac{83}{18}=100$$

Add \frac{83}{18} to both sides.

$$\frac{19}{18}t_{0}=100+\frac{83}{18}$$

Add 100 and \frac{83}{18} to get \frac{1883}{18}.

$$\frac{19}{18}t_{0}=\frac{1883}{18}$$

Multiply both sides by \frac{18}{19}, the reciprocal of \frac{19}{18}.

$$t_{0}=\frac{1883}{18}\times \frac{18}{19}$$

Multiply \frac{1883}{18} and \frac{18}{19} to get \frac{1883}{19}.

$$t_{0}=\frac{1883}{19}$$