Video: US-SAT05S3-Q07-527159489176

Jack started a freelance job. He earned $100 on the first day, $60 on the second day, and $150 on the third day. His goal is to earn an average of at least $120 per day for 4 days. Which inequality can be used to represent the amount of money, 𝑥, that Jack could earn on the 4th day for him to meet his goal? [A] 100 + 60 + 150 + 𝑥 ≥ 4(120) [B] (100/4) + (60/4) + (150/4) + 𝑥 ≥ 120 [C] ((100 + 60 + 150)/3) + 𝑥 ≥ 120 [D] 100 + 60 + 150 ≥ 𝑥(120)

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Video Transcript

Jack started a freelance job. He earned 100 dollars on the first day, 60 dollars on the second day, and 150 dollars on the third day. His goal is to earn an average of at least 120 dollars per day for four days. Which inequality can be used to represent the amount of money, 𝑥, that Jack needs to earn on the fourth day for him to meet his goal? A) 100 plus 60 plus 150 plus 𝑥 is greater than or equal to four times 120. B) 100 over four plus 60 over four plus 150 over four plus 𝑥 is greater than or equal to 120. C) 100 plus 60 plus 150 divided by three plus 𝑥 is greater than or equal to 120. D) 100 plus 60 plus 150 is greater than or equal to 𝑥 times 120.

First, let’s write out what Jack’s goal is. He needs to average at least 120 dollars for four days. If you take the sum of all values and divide it by the number of values, you’ll get the average. The money Jack earned in day one plus the money Jack earned in day two plus the money Jack earned in day three plus the money Jack earned in day four will be the sum of all his money for the four days. There are four days. And this value, this average, needs to be greater than or equal to 120. The minimum average is 120, but it could be greater.

Let’s substitute what we know for days one through four. We now have an inequality 100 plus 60 plus 150 plus 𝑥 divided by four has to be greater than or equal to 120. However, none of the answer choices match this inequality. So we’ll need to do some rearranging. We could multiply both sides of the inequality by four. And then we would have 𝑥 plus 60 plus 150 plus 𝑥 is greater than or equal to four times 120, which is answer choice A.

Answer choice B is pretty close. If it had 𝑥 divided by four, if all four of these terms were being divided by four, it could be a viable option. But since it doesn’t have 𝑥 divided by four, it’s incorrect. Option C is averaging the first three days and then adding 𝑥 and this would not yield a correct value for 𝑥. And option D is saying that the money made in the first three days added together must be greater than the money he made on day four multiplied by 120. Which doesn’t make sense. Only option A will help Jack calculate how much money he needs to earn on day four to meet his goal of an average of at least 120 dollars for the four days.

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