Chapter 6.3, Problem 36E

To determine

Tofind the three ways to solve a proportion

Answer to Problem 36E

After applying the first method that is cross products property the answer will be $\text{x = 24}$

After applying the second method which is algebraic method answer will be $\text{x = 24}$

And after applying the third method which is ratio method the answer will be same $\text{x = 24}$

Explanation of Solution

Given information :

Consider the ratio $\frac{6}{10}=\frac{\text{x}}{40}$

Calculations:

apply cross products property to evaluate the given variable then divide both sides of the equations with 10 to isolate the variable on 1 side of the equation

Therefore,

The equation will be

  $\begin{array}{l}\frac{6}{10}=\frac{\text{x}}{40}\\ \text{ 6}\times \text{40 = x}\times \text{10}\\ \frac{6\times 40}{10}\text{=x }\\ \text{ x=24 }\end{array}$

Apply algebraic method to evaluate the given variable the multiply both sides of the equations with 40 to isolate the variable on 1 side of the equation

Therefore ,

The equation will be

  $\begin{array}{l}\frac{6}{10}\times 40=\frac{\text{x}}{40}\times 40\\ \frac{6}{1}\times 4=\text{x}\\ \text{x = 24}\end{array}$

Apply the ratio method to evaluate the given variable evaluate the common ratio by dividing the dinominators, then the numerator 40 should be 4 times that of numerator 10

Therefore,

The ratio becomes

  $\begin{array}{l}\frac{40}{10}=4\\ \text{x = 6}\times \text{ 4}\\ \text{x = 24}\end{array}$

Therefore,After applying the first method that is cross products property the answer will be $\text{x = 24}$

After applying the second method which is algebraic method answer will be

  $\text{x = 24}$

And after applying the third method which is ratio method the answer will be same

  $\text{x = 24}$