Solve 100/(x+20)=60/(70-x)

$$\frac { 100 } { ( x + 20 ) } = \frac { 60 } { ( 70 - x ) }$$

Solve for x

$$x = \frac{145}{4} = 36\frac{1}{4} = 36.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -20,70 since division by zero is not defined. Multiply both sides of the equation by \left(x-70\right)\left(x+20\right), the least common multiple of x+20,70-x.

$$\left(x-70\right)\times 100=-\left(20+x\right)\times 60$$

Use the distributive property to multiply x-70 by 100.

$$100x-7000=-\left(20+x\right)\times 60$$

Multiply -1 and 60 to get -60.

$$100x-7000=-60\left(20+x\right)$$

Use the distributive property to multiply -60 by 20+x.

$$100x-7000=-1200-60x$$

Add 60x to both sides.

$$100x-7000+60x=-1200$$

Combine 100x and 60x to get 160x.

$$160x-7000=-1200$$

Add 7000 to both sides.

$$160x=-1200+7000$$

Add -1200 and 7000 to get 5800.

$$160x=5800$$

Divide both sides by 160.

$$x=\frac{5800}{160}$$

Reduce the fraction \frac{5800}{160} to lowest terms by extracting and canceling out 40.

$$x=\frac{145}{4}$$