Solve 85.82=75.3[1+(1.70*10^-4)(T-27)]

$$85.82 = 75.3 [ 1 + ( 1.70 \times 10 ^ { - 4 } ) ( T - 27 ) ]$$

Solve for T

$$T = \frac{10865627}{12801} = 848\frac{10379}{12801} \approx 848.810796032$$

Steps for Solving Linear Equation

Divide both sides by 75.3.

$$\frac{85.82}{75.3}=1+1.7\times 10^{-4}\left(T-27\right)$$

Expand \frac{85.82}{75.3} by multiplying both numerator and the denominator by 100.

$$\frac{8582}{7530}=1+1.7\times 10^{-4}\left(T-27\right)$$

Reduce the fraction \frac{8582}{7530} to lowest terms by extracting and canceling out 2.

$$\frac{4291}{3765}=1+1.7\times 10^{-4}\left(T-27\right)$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{4291}{3765}=1+1.7\times \frac{1}{10000}\left(T-27\right)$$

Multiply 1.7 and \frac{1}{10000} to get \frac{17}{100000}.

$$\frac{4291}{3765}=1+\frac{17}{100000}\left(T-27\right)$$

Use the distributive property to multiply \frac{17}{100000} by T-27.

$$\frac{4291}{3765}=1+\frac{17}{100000}T-\frac{459}{100000}$$

Subtract \frac{459}{100000} from 1 to get \frac{99541}{100000}.

$$\frac{4291}{3765}=\frac{99541}{100000}+\frac{17}{100000}T$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{99541}{100000}+\frac{17}{100000}T=\frac{4291}{3765}$$

Subtract \frac{99541}{100000} from both sides.

$$\frac{17}{100000}T=\frac{4291}{3765}-\frac{99541}{100000}$$

Subtract \frac{99541}{100000} from \frac{4291}{3765} to get \frac{10865627}{75300000}.

$$\frac{17}{100000}T=\frac{10865627}{75300000}$$

Multiply both sides by \frac{100000}{17}, the reciprocal of \frac{17}{100000}.

$$T=\frac{10865627}{75300000}\times \frac{100000}{17}$$

Multiply \frac{10865627}{75300000} and \frac{100000}{17} to get \frac{10865627}{12801}.

$$T=\frac{10865627}{12801}$$