Solve 100-87/87-81=frac{100-{t}_{0}}{{t}_{0}-83}

$$\frac{ 100-87 }{ 87-81 } = \frac{ 100- { t }_{ 0 } }{ { t }_{ 0 } -83 }$$

Solve for t_0

$$t_{0} = \frac{1679}{19} = 88\frac{7}{19} \approx 88.368421053$$

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.

$$\left(\frac{1}{6}t_{0}-\frac{83}{6}\right)\left(100-87\right)=100-t_{0}$$

Subtract 87 from 100 to get 13.

$$\left(\frac{1}{6}t_{0}-\frac{83}{6}\right)\times 13=100-t_{0}$$

Use the distributive property to multiply \frac{1}{6}t_{0}-\frac{83}{6} by 13.

$$\frac{13}{6}t_{0}-\frac{1079}{6}=100-t_{0}$$

Add t_{0} to both sides.

$$\frac{13}{6}t_{0}-\frac{1079}{6}+t_{0}=100$$

Combine \frac{13}{6}t_{0} and t_{0} to get \frac{19}{6}t_{0}.

$$\frac{19}{6}t_{0}-\frac{1079}{6}=100$$

Add \frac{1079}{6} to both sides.

$$\frac{19}{6}t_{0}=100+\frac{1079}{6}$$

Add 100 and \frac{1079}{6} to get \frac{1679}{6}.

$$\frac{19}{6}t_{0}=\frac{1679}{6}$$

Multiply both sides by \frac{6}{19}, the reciprocal of \frac{19}{6}.

$$t_{0}=\frac{1679}{6}\times \frac{6}{19}$$

Multiply \frac{1679}{6} and \frac{6}{19} to get \frac{1679}{19}.

$$t_{0}=\frac{1679}{19}$$