Solve 160/(30-t)=191/(90-t)

$$\frac { 160 } { ( 30 - t ) } = \frac { 191 } { ( 90 - t ) }$$

Solve for t

$$t = -\frac{8670}{31} = -279\frac{21}{31} \approx -279.677419355$$

Steps for Solving Linear Equation

Variable t cannot be equal to any of the values 30,90 since division by zero is not defined. Multiply both sides of the equation by \left(t-90\right)\left(t-30\right), the least common multiple of 30-t,90-t.

$$\left(90-t\right)\times 160=\left(30-t\right)\times 191$$

Use the distributive property to multiply 90-t by 160.

$$14400-160t=\left(30-t\right)\times 191$$

Use the distributive property to multiply 30-t by 191.

$$14400-160t=5730-191t$$

Add 191t to both sides.

$$14400-160t+191t=5730$$

Combine -160t and 191t to get 31t.

$$14400+31t=5730$$

Subtract 14400 from both sides.

$$31t=5730-14400$$

Subtract 14400 from 5730 to get -8670.

$$31t=-8670$$

Divide both sides by 31.

$$t=\frac{-8670}{31}$$

Fraction \frac{-8670}{31} can be rewritten as -\frac{8670}{31} by extracting the negative sign.

$$t=-\frac{8670}{31}$$