Chapter 6.1, Problem 47HP

To determine

Find whether the expression will always, sometimes, or never equivalent.

Answer to Problem 47HP

The both the expression will always equivalent.

Explanation of Solution

Given:

It is given in the question that the expression is $x\%ofy$ and $y\%ofx$ .

Concept Used:

In this, use the concept of percent proportion such that the ratio of given two number will equal to the ratio of $p/100$ .

Calculation:

Suppose there’s some value of a so that a is $x\%$ of y and $y\%ofx$ . That gives us the proportion.

  $\frac{a}{y}=\frac{x}{100}(i)$

  $\frac{a}{x}=\frac{y}{100}(ii)$

Let’s solve both equations for a . Notice that it become the same equation. Also note that this is true for any a , including $a=0$ .

  $a=\frac{xy}{100}(Equationi)$

  $a=\frac{xy}{100}(Equationii)$

Both are equivalent.

Conclusion:

The both the expression will always equivalent.