Video: Solving Word Problems Involving Percentages

Scarlett spent 58 hours studying English and biology this month. She spent 36 hours studying English. Which of the following is the closest approximation for the percentage of hours she spent studying biology? [A] 18 2/3% [B] 23 1/3% [C] 33 1/3% [D] 48 1/3% [E] 66 2/3%

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Video Transcript

Scarlett spent 58 hours studying English and biology this month. She spent 36 hours studying English. Which of the following is the closest approximation for the percentage of hours she spent studying biology?

The amount of time that Scarlett spent studying both subjects was 58 hours. Of this 58 hours, she spent 36 of them studying English. In order to calculate the number of hours she spent studying biology, we need to subtract 36 from 58. 58 minus 36 is equal to 22. This means that Scarlett spent 22 hours studying biology.

We were asked to calculate the percentage of hours that she spent studying biology. The fraction of time she spent studying biology is 22 out of 58 or twenty-two fifty-eighths. This is because she spent 22 hours studying biology and 58 hours studying all together.

To turn any fraction into a percentage, we need to multiply by 100. Therefore, we need to multiply twenty-two fifty-eighths by 100. Typing this into the calculator gives us 37.93103, and so on. If we want to round this to one decimal place, the three is the deciding number. As this is less than five, we’ll round down. The percentage of hours that Scarlett spent studying biology is 37.9 percent to one decimal place.

We were asked to find the closest approximation out of the five options. As the options are in ascending order, we can see that 37.9 percent lies between 33 and a third percent and 48 and a third percent. This means we can immediately rule out option A, option B, and option E.

It is clear from the number line or by estimating that 37.9 percent is closer to 33 and a third percent than it is to 48 and a third percent. 37.9 percent is less than five percent away from 33 and a third. But it is more than 10 away from 48 and one-third.

This means that the closest approximation for the percentage of hours that Scarlett spent studying biology is 33 and one-third percent.

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