Question

Is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? Explain.

Answer 1

Answer:

No. The amounts of change are the same, but the original amounts are different. The ratio for the percent increase from 50 to 70 is 20/50, or 40%. The ratio for the percent decrease from 70 to 50 is 20/70, or about 29%.

Answer 2

The percent increase and the percent decrease are not the same because in percent increase we are diving the change in the numbers by the smaller number while in percent decrease we are diving the change in the numbers by the bigger number.

The given parameters;

• percent increase from 50 to 70
• percent decrease from 70 to 50

The percentage increase from 50 to 70 is calculated as;

increase in the number: = 70 - 50 = 20

$\% \ increase= \frac{increase}{smaller \ number}\times 100\% \\\\= \frac{20}{50} \times 100\% \\\\= 40\%$

The percentage decrease from 70 to 50 is calculated as;

decrease in the number: 70 - 50 = 20

$\% \ decrease= \frac{increase}{bigger \ number}\times 100\% \\\\= \frac{20}{70} \times 100\% \\\\= 28.6 \%$

Thus, the percent increase and the percent decrease are not the same because in percent increase we are diving the change in the numbers by the smaller number while in percent decrease we are diving the change in the numbers by the bigger number.

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