Solve 80-74/74-61=frac{100-{t}_{0}}{{t}_{0}-83}

$$\frac{ 80-74 }{ 74-61 } = \frac{ 100- { t }_{ 0 } }{ { t }_{ 0 } -83 }$$

Solve for t_0

$$t_{0} = \frac{1798}{19} = 94\frac{12}{19} \approx 94.631578947$$

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.

$$\left(\frac{1}{13}t_{0}-\frac{83}{13}\right)\left(80-74\right)=100-t_{0}$$

Subtract 74 from 80 to get 6.

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

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

$$\frac{6}{13}t_{0}-\frac{498}{13}=100-t_{0}$$

Add t_{0} to both sides.

$$\frac{6}{13}t_{0}-\frac{498}{13}+t_{0}=100$$

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

$$\frac{19}{13}t_{0}-\frac{498}{13}=100$$

Add \frac{498}{13} to both sides.

$$\frac{19}{13}t_{0}=100+\frac{498}{13}$$

Add 100 and \frac{498}{13} to get \frac{1798}{13}.

$$\frac{19}{13}t_{0}=\frac{1798}{13}$$

Multiply both sides by \frac{13}{19}, the reciprocal of \frac{19}{13}.

$$t_{0}=\frac{1798}{13}\times \frac{13}{19}$$

Multiply \frac{1798}{13} and \frac{13}{19} to get \frac{1798}{19}.

$$t_{0}=\frac{1798}{19}$$