Video: Solving Word Problems Involving Percentage

A collector sold his artifacts to 40% of the people who attended the auction. If 90 people attended the auction, determine how many people the collector sold his artifacts to.

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Video Transcript

A collector sold his artifacts to 40 percent of the people who attended the auction. If 90 people attended the auction, determine how many people the collector sold his artifacts to.

In order to answer this question, we need to calculate 40 percent of 90, as 40 percent of the people were sold artifacts. We will solve this problem using a noncalculator and calculator method.

In order to solve this problem without a calculator, we need to consider the total number of people, in this case 90. This will be equal to 100 percent. We can then scale this number up or down until we reach the value for 40 percent.

Remember whatever you do to one side of an equation, you must do to the other. Dividing both sides of the equation by 10 gives us 10 percent is equal to nine as 100 divided by 10 is equal to 10. And 90 divided by 10 is equal to nine.

Multiplying both sides of this equation by four gives us 40 percent on the left-hand side as 10 percent multiplied by four is equal to 40 percent. Nine multiplied by four is equal to 36. Therefore, 40 percent of the 90 people is equal to 36. We can, therefore, say that the collector sold his artifacts to 36 people.

We could also solve this problem on a calculator using the fact that 40 percent is equal to 0.4 as a decimal and 40 over 100 or 40 hundredths as a fraction.

The word “of” in maths usually means multiply or times. This means that we could rewrite 40 percent of 90 as either 0.4 multiplied by 90 or 40 one hundredths multiplied by 90. 0.4 multiplied by 90 is equal to 36. And 40 one hundredths multiplied by 90 is also equal to 36. Both of these answers are the same as the noncalculator method.

The number of people is equal to 36.

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