Video: Solving Word Problems Involving Percentage

Mr. Matthew surveyed 302 students regarding their favorite kind of juice. The table shows the results of the survey. Which of the following is the best estimate for the number of students who prefer mixed fruit? [A] 30 students [B] 60 students [C] 90 students [D] 120 students [E] 210 students

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Video Transcript

Mr. Matthew surveyed 302 students regarding their favorite kind of juice. The table shows the results of the survey. Which of the following is the best estimate for the number of students who prefer mixed fruit? Is it 30, 60, 90, 120, or 210 students?

The key word here is estimate. We will show you how to work out the exact value. But firstly, we need to focus on an estimate. An estimate is an educated guess using rounding. As they were 302 students in the survey, we can round this to 300. In the same way, the percent of students that said mixed fruit was 29 percent. This can be rounded to 30 percent. Both of these numbers have been rounded to one significant figure as they have one nonzero term.

To answer the question, we now need to find 30 percent of 300. The total value is 300. Therefore, we can say that 100 hundred percent is equal to 300. Dividing both sides of this equation by 10 tells us that 10 percent of the students equals 30. 10 percent multiplied by three is equal to 30 percent. Multiplying the other side of the equation by three gives us 90. As 30 multiplied by three is equal to 90, we can therefore say that 30 percent of 300 is equal to 90 students.

The best estimate for the number of students who prefer mixed fruit is 90 students. We could work out the exact value by working out 29 percent of 302. The word of in maths usually means times or multiply. We know that 29 percent is the same as 0.29 or twenty-nine hundredths. We could therefore multiply either of these by 302 to calculate the exact number of students. 0.29 multiplied by 302 is 87.58. Therefore, 29 percent of 302 is also 87.58.

As we can only have a whole number of students, we need to round this number. As the five after the decimal point is five or greater, we will round up. Therefore, 88 students said that their favorite juice was mixed fruit. As 88 is closer to 90 than any of our other options, we know that our initial estimate of 90 students is correct.

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