Solve frac{k_{2}}{k_{1}}=80/100*(1.25)^2

$$\frac { k _ { 2 } } { k _ { 1 } } = \frac { 80 } { 100 } \times ( 1.25 ) ^ { 2 }$$

Solve for k_1

$$k_{1}=\frac{4k_{2}}{5}$$

$$k_{2}\neq 0$$

Steps for Solving Linear Equation

Variable k_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 100k_{1}, the least common multiple of k_{1},100.

$$100k_{2}=k_{1}\times 80\times 1.25^{2}$$

Calculate 1.25 to the power of 2 and get 1.5625.

$$100k_{2}=k_{1}\times 80\times 1.5625$$

Multiply 80 and 1.5625 to get 125.

$$100k_{2}=k_{1}\times 125$$

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

$$k_{1}\times 125=100k_{2}$$

The equation is in standard form.

$$125k_{1}=100k_{2}$$

Divide both sides by 125.

$$\frac{125k_{1}}{125}=\frac{100k_{2}}{125}$$

Dividing by 125 undoes the multiplication by 125.

$$k_{1}=\frac{100k_{2}}{125}$$

Divide 100k_{2} by 125.

$$k_{1}=\frac{4k_{2}}{5}$$

Variable k_{1} cannot be equal to 0.

$$k_{1}=\frac{4k_{2}}{5}\text{, }k_{1}\neq 0$$

Solve for k_2

$$k_{2}=\frac{5k_{1}}{4}$$

$$k_{1}\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 100k_{1}, the least common multiple of k_{1},100.

$$100k_{2}=k_{1}\times 80\times 1.25^{2}$$

Calculate 1.25 to the power of 2 and get 1.5625.

$$100k_{2}=k_{1}\times 80\times 1.5625$$

Multiply 80 and 1.5625 to get 125.

$$100k_{2}=k_{1}\times 125$$

The equation is in standard form.

$$100k_{2}=125k_{1}$$

Divide both sides by 100.

$$\frac{100k_{2}}{100}=\frac{125k_{1}}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$k_{2}=\frac{125k_{1}}{100}$$

Divide 125k_{1} by 100.

$$k_{2}=\frac{5k_{1}}{4}$$