Video: US-SAT04S4-Q22-723187861465

The given bar graph shows the consumption, in millions of tons, of several fabric materials in 2010 and 2019 in a factory in the United States. Which of the following best approximates the percentage decrease in the consumption of cotton in the United States from 2010 - 2019? [A] 10% [B] 8% [C] 25% [D] 37%

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Video Transcript

The given bar graph shows the consumption, in millions of tons, of several fabric materials in 2010 and 2019 in a factory in the United States. Which of the following best approximates the percentage decrease in the consumption of cotton in the United States from 2010 to 2019? A) 10 percent, B) 8 percent, C) 25 percent, or D) 37 percent.

Before we can solve this, we need to know what a percentage decrease is. A percent decrease is the decrease amount over the original amount multiplied by 100. It’s a comparison of how much something went down compared to how much it originally was. We want to know about the percent decrease of cotton. In 2010, there was a usage of 2.5 million tons. And now, we need to estimate the cotton usage in 2019. We see that it’s between 2.0 and 2.5 and it’s closer to 2.5. We could draw a line that represents halfway between 2.0 and 2.5 and use this line to help inform our estimate. Halfway between 2.0 and 2.5 is 2.25. And the cotton usage is slightly more than 2.25. And so, we can estimate a usage of 2.3 million tons.

If in 2010, there was usage of 2.5 million and in 2019, there was a usage of 2.3 million, we’ll subtract 2.3 from 2.5 and then divide that by the original amount. That’s the 2010 amount of 2.5. Whatever we get here, we need to multiply by 100 percent. We would have 0.2 over 2.5, which reduces to 0.08 If we multiply that by 100, we get eight percent, which is option B.

Now I want to consider what would have happened if you have not estimated the 2019 value to be 2.3. For example, what if you estimated that value to be 2.35? In that case, you would need to subtract 2.35 from 2.5. The original stays the same as 2.5 When you do that, you get 0.15 over 2.5, which comes to 0.06. And remember, we multiply that value by 100. An estimate of 2.35 gives you a percent decrease of six percent.

Remember in the question, it asked for the best approximate. And six percent is closest to eight percent out of the four answer choices. So even if your estimate was slightly different than mine, you’ll still get close enough to see that eight percent is a good approximation for the percent decrease.

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