Q46. - Algebra 1

Question

If you have 75% of a number n, what percent of decrease is it from the number n? If you have 40% of a number a, what percent of decrease do you have from the number a? What pattern do you notice? Is this always true?

Step-by-Step Solution

Answer

The percent of decreases from the number $n=25\%$ and $a=60\%$, thus the total percent is always 100.

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Simplify the expression.

The given expression is 75% of a number n and since the total percentage is always 100 we must have a decrease of $100\%-75\%=25\%$ 

Also, 40% of a number  means the decrease will be $100\%-40\%=60\%$

Therefore, the percent of decrease is it from the number $n=25\%$ and $a=60\%$ the total percent is always 100.