Solve (100-x)80=(100(1-4%)-x)(80-4*4)

$$(100-x)80=(100(1-4 \% )-x)(80-4 \times 4)$$

Solve for x

$$x=116$$

Steps for Solving Linear Equation

Use the distributive property to multiply 100-x by 80.

$$8000-80x=\left(100\left(1-\frac{4}{100}\right)-x\right)\left(80-4\times 4\right)$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$8000-80x=\left(100\left(1-\frac{1}{25}\right)-x\right)\left(80-4\times 4\right)$$

Convert 1 to fraction \frac{25}{25}.

$$8000-80x=\left(100\left(\frac{25}{25}-\frac{1}{25}\right)-x\right)\left(80-4\times 4\right)$$

Since \frac{25}{25} and \frac{1}{25} have the same denominator, subtract them by subtracting their numerators.

$$8000-80x=\left(100\times \frac{25-1}{25}-x\right)\left(80-4\times 4\right)$$

Subtract 1 from 25 to get 24.

$$8000-80x=\left(100\times \frac{24}{25}-x\right)\left(80-4\times 4\right)$$

Express 100\times \frac{24}{25} as a single fraction.

$$8000-80x=\left(\frac{100\times 24}{25}-x\right)\left(80-4\times 4\right)$$

Multiply 100 and 24 to get 2400.

$$8000-80x=\left(\frac{2400}{25}-x\right)\left(80-4\times 4\right)$$

Divide 2400 by 25 to get 96.

$$8000-80x=\left(96-x\right)\left(80-4\times 4\right)$$

Multiply 4 and 4 to get 16.

$$8000-80x=\left(96-x\right)\left(80-16\right)$$

Subtract 16 from 80 to get 64.

$$8000-80x=\left(96-x\right)\times 64$$

Use the distributive property to multiply 96-x by 64.

$$8000-80x=6144-64x$$

Add 64x to both sides.

$$8000-80x+64x=6144$$

Combine -80x and 64x to get -16x.

$$8000-16x=6144$$

Subtract 8000 from both sides.

$$-16x=6144-8000$$

Subtract 8000 from 6144 to get -1856.

$$-16x=-1856$$

Divide both sides by -16.

$$x=\frac{-1856}{-16}$$

Divide -1856 by -16 to get 116.

$$x=116$$