Chapter 7.3, Problem 44STP

To determine

To find: the required number

Answer to Problem 44STP

Option J, 28 is the number

Explanation of Solution

Given:

40% of number is 32

Find: 35% of the number

1. 8
2. 20
3. 24
4. 28

Calculation:

Let n represent the number.

  $\begin{array}{l}\frac{32}{n}=\frac{40}{100}\text{ Write the percent proportion}\\ 32\times 100=n\times 40\text{ Find the cross product}\\ \text{ 3200=40}n\text{ Multiply}\\ \frac{\text{3200}}{40}=\frac{40n}{40}\text{ Divide each side by 40}\text{.}\\ \text{ 80}=n\text{ Simplify}\end{array}$

So, 40% of 80 is 32.

Let m is the part.

  $\begin{array}{l}\frac{m}{80}=\frac{35}{100}\\ m\times 100=80.35\\ 100m=2800\\ \frac{100m}{100}=\frac{2800}{100}\\ m=28\end{array}$

Therefore, 35% of 80 is 28.

Conclusion:

Thus, option J, 28 is the number