Video: US-SAT04S4-Q04-684173530290

Tommy surveyed a random sample of coworkers at his company to determine whether the Christmas party should be held indoors or outdoors. Of the 70 coworkers surveyed, 34.7% preferred that it be held indoors. Based on this information, about how many coworkers in the entire 340-person company are expected to prefer that the Christmas party would be held indoors? [A] 130 [B] 125 [C] 110 [D] 120

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Video Transcript

Tommy surveyed a random sample of coworkers at his company to determine whether the Christmas party should be held indoors or outdoors. Of the 70 coworkers surveyed, 34.7 percent preferred that it be held indoors. Based on this information, about how many coworkers in the entire 340-person company are expected to prefer that the Christmas party would be held indoors. Is it 130, 125, 110, or 120?

We are told that 34.7 percent of the coworkers surveyed would prefer the Christmas party to take place indoors. As there are 340 people working at the company in total, the quickest way to work out an estimate would be to calculate 34.7 percent of 340. The word “of” in mathematics means multiply or times. The word percent means out of 100. Therefore, 34.7 percent is the same as 34.7 over or divided by 100. Dividing by 100 moves all of our digits two places to the right. This means that 34.7 divided by 100 is equal to 0.347. We need to multiply this decimal by 340. Typing this into our calculator gives us an answer of 117.98. To the nearest whole number, this would be 118 coworkers.

However, this is not one of the four options. Our four options were 130, 125, 110, and 120. 117.98 is closest to 120. Therefore, this is the best approximation for the number of coworkers that would prefer that the Christmas party would be held indoors. We can also see this on a number line. 117.98 rounded to the nearest five is 120.

An alternative method would be to calculate 34.7 percent of 70. This would tell us how many of the coworkers that were surveyed would prefer that the Christmas party was held indoors. 0.347 multiplied by 70 is equal to 24.29. As we can only have a whole number of people, we need to round this to the nearest whole number. 24.29 rounds down to 24. Therefore, 24 out of the 70 coworkers would prefer the Christmas party to be held indoors.

We need to scale this up so that we have a number out of 340. 340 is approximately five times as many as 70 as 70 multiplied by five equals 350. We can therefore multiply 24 by five to work out the approximation. 20 multiplied by five is 100. And four multiplied by five is 20. Therefore, 24 multiplied by five is 120. Once again, we can see that 120 out of the 340-person workforce would prefer the Christmas party to be held indoors.

The correct answer is option D, 120.

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