Chapter 3.7, Problem 87STP

To determine

To find: The 75% percentage of what number is 90.

Answer to Problem 87STP

The required number is 120.

Explanation of Solution

Given information:

The 75% of requirednumber is 90.

Concept used:

The r% of x is y implies $x\times \frac{r}{100}=y$ .

Calculations:

The 75% of required number is 90.

Let the 75% of a number x is 90.

  $\Rightarrow x\times \frac{75}{100}=90$

Thus, the statement of the problem is an equation

  $\frac{75x}{100}=90$ … (1)

Now, we solve equation (1) that is $\frac{\stackrel{3}{\cancel{75}}x}{{\cancel{100}}_4}=90$

  $\Rightarrow \frac{3x}{4}=90$

  $\Rightarrow \frac{3x}{4}\times 4=90\times 4$  Multiplying both sides by 4

  $\Rightarrow \frac{3x}{\cancel{4}}\times \cancel{4}=90\times 4$

  $\Rightarrow 3x=90\times 4$

  $\Rightarrow \frac{3x}{3}=\frac{90\times 4}{3}$  Dividing each side by 3

  $\Rightarrow \frac{\cancel{3}x}{\cancel{3}}=\frac{\stackrel{30}{\cancel{90}}\times 4}{\cancel{3}}$

  $\Rightarrow x=30\times 4$

  $\Rightarrow x=120$

Thus, the 75% of 120 is 90.

Conclusion:

The75% of 120 is 90.