Solve 0.1*380*(100-29.5)=0.15x(29.5-20)+0.04*380*(29.5-20)

$$0.1 \times 380 \times (100-29.5)=0.15x(29.5-20)+0.04 \times 380 \times (29.5-20)$$

Solve for x

$$x = \frac{5336}{3} = 1778\frac{2}{3} \approx 1778.666666667$$

Steps for Solving Linear Equation

Multiply 0.1 and 380 to get 38.

$$38\left(100-29.5\right)=0.15x\left(29.5-20\right)+0.04\times 380\left(29.5-20\right)$$

Subtract 29.5 from 100 to get 70.5.

$$38\times 70.5=0.15x\left(29.5-20\right)+0.04\times 380\left(29.5-20\right)$$

Multiply 38 and 70.5 to get 2679.

$$2679=0.15x\left(29.5-20\right)+0.04\times 380\left(29.5-20\right)$$

Subtract 20 from 29.5 to get 9.5.

$$2679=0.15x\times 9.5+0.04\times 380\left(29.5-20\right)$$

Multiply 0.15 and 9.5 to get 1.425.

$$2679=1.425x+0.04\times 380\left(29.5-20\right)$$

Multiply 0.04 and 380 to get 15.2.

$$2679=1.425x+15.2\left(29.5-20\right)$$

Subtract 20 from 29.5 to get 9.5.

$$2679=1.425x+15.2\times 9.5$$

Multiply 15.2 and 9.5 to get 144.4.

$$2679=1.425x+144.4$$

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

$$1.425x+144.4=2679$$

Subtract 144.4 from both sides.

$$1.425x=2679-144.4$$

Subtract 144.4 from 2679 to get 2534.6.

$$1.425x=2534.6$$

Divide both sides by 1.425.

$$x=\frac{2534.6}{1.425}$$

Expand \frac{2534.6}{1.425} by multiplying both numerator and the denominator by 1000.

$$x=\frac{2534600}{1425}$$

Reduce the fraction \frac{2534600}{1425} to lowest terms by extracting and canceling out 475.

$$x=\frac{5336}{3}$$