Video: Solving Word Problems Involving Percentages

A book club had 60 members last year. This year, it has 48 members. Determine the percentage decrease in the number of club members.

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Video Transcript

A book club had 60 members last year. This year, it has 48 members. Determine the percentage decrease in the number of club members.

A percentage decrease is equal to the amount of the decrease divided by the original amount multiplied by 100. The first part of this calculation gives the proportion of the original amount that the decrease represents. The second part converts it from a decimal to a percentage. Let’s look at the numbers in this question.

The book club had 60 members last year. So the original amount is equal to 60. The book club now has only 48 members. Therefore, the amount of the decrease is equal to the difference between these two values: 60 minus 48 which is 12. Substituting each of these values into the calculation gives that the percentage decrease is equal to 12 over 60 multiplied by 100.

12 and 60 both share a factor of 12 and so they can be cancelled by this amount, giving one in the numerator and five in the denominator. The calculation therefore simplifies to 100 over five, which is equal to 20. The percentage decrease is 20 percent.

Now, there is a common error to watch out for when calculating percentage increase or decrease. Remember that the formula for percentage decrease tells us that we should be dividing by the original amount. The common error is to divide instead by the new amount, which in this case would be 48, giving an answer of 25 percent.

Watch out for this when you are answering questions about percentage change. The amount you divide by must be the original amount, not the new amount.

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