Chapter 6.1, Problem 31IP

a.

To determine

Explain the pattern of the percentage and its number.

Answer to Problem 31IP

The percentage are always doubled, while the total values are divided by $2$ .

Explanation of Solution

Given:

It is given in the question that the following expressions are:

  $2\%of100=2$

  $4\%of50=2$

  $8\%of25=2$

  $16\%of12.5=2$

Here, The following pattern will follow:

  $2\%\stackrel{\times 2}{\to }4\%\stackrel{\times 2}{\to }8\%\stackrel{\times 2}{\to }16\%$

  $100\stackrel{÷2}{\to }50\stackrel{÷2}{\to }25\stackrel{÷2}{\to }12.5$

So, here the percentage are always doubled, while the total values are divided by $2$ .

b.

To determine

Calculate the next equation in the pattern.

Answer to Problem 31IP

The next equation in the pattern is $32\%of6.25=2$ .

Explanation of Solution

Given:

It is given in the question that the following expressions are:

  $2\%of100=2$

  $4\%of50=2$

  $8\%of25=2$

  $16\%of12.5=2$

Concept Used:

In this, use the concept of understanding the pattern.

Calculation: Here, the pattern follows the following: The percentage are always doubled, while the total values are divided by $2$ .

  $16\%\times 2=32\%$

  $12.5÷2=6.25$

So, from both $32\%of6.25=2$

Conclusion:

The next term is $32\%of6.25=2$ .