Solve 500*4.18left(T-20right)=120*0.95left(100-Tright)

$$500 \cdot 4.18 \left( T-20 \right) = 120 \cdot 0.95 \left( 100-T \right)$$

Solve for T

$$T = \frac{700}{29} = 24\frac{4}{29} \approx 24.137931034$$

Steps for Solving Linear Equation

Multiply 500 and 4.18 to get 2090.

$$2090\left(T-20\right)=120\times 0.95\left(100-T\right)$$

Use the distributive property to multiply 2090 by T-20.

$$2090T-41800=120\times 0.95\left(100-T\right)$$

Multiply 120 and 0.95 to get 114.

$$2090T-41800=114\left(100-T\right)$$

Use the distributive property to multiply 114 by 100-T.

$$2090T-41800=11400-114T$$

Add 114T to both sides.

$$2090T-41800+114T=11400$$

Combine 2090T and 114T to get 2204T.

$$2204T-41800=11400$$

Add 41800 to both sides.

$$2204T=11400+41800$$

Add 11400 and 41800 to get 53200.

$$2204T=53200$$

Divide both sides by 2204.

$$T=\frac{53200}{2204}$$

Reduce the fraction \frac{53200}{2204} to lowest terms by extracting and canceling out 76.

$$T=\frac{700}{29}$$