Video: SAT Practice Test 1 • Section 4 • Question 9

A company produces and sells a certain product. The cost 𝐶 of producing 𝑥 units is 𝐶 = 15𝑥 + 1710, and the company sells the product at $45 per unit. The company will make a profit only if the total revenue from selling 𝑥 units is greater than the total cost of producing 𝑥 units. Which of the following inequalities gives the number of units 𝑥 that the company needs to sell in order to make a profit? [A] 𝑥 > 57 [B] 𝑥 < 57 [C] 𝑥 > 38 [D] 𝑥 < 38

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Video Transcript

A company produces and sells a certain product. The cost 𝐶 of producing 𝑥 units is 𝐶 is equal to 15𝑥 plus 1710. And the company sells the product at 45 dollars per unit. The company will make a profit only if the total revenue from selling 𝑥 units is greater than the total cost of producing 𝑥 units. Which of the following inequalities gives the number of units 𝑥 that the company needs to sell in order to make a profit? Is it A) 𝑥 is greater than 57, B) 𝑥 is less than 57, C) 𝑥 is greater than 38, or D) 𝑥 is less than 38?

As the company sells the product for 45 dollars per unit, the revenue will be equal to 45 multiplied by 𝑥, written 45𝑥. We were told in the question that the cost, 𝐶, is equal to 15𝑥 plus 1710. The company will make a profit if the revenue is greater than the cost.

In this particular question, 45𝑥 needs to be greater than 15𝑥 plus 1710. In order to balance this inequality, we can subtract 15𝑥 from both sides. 45𝑥 minus 15𝑥 is equal to 30𝑥. Subtracting 15𝑥 from the right-hand side leaves us with 1710.

Our final step is to divide both sides of the inequality by 30. 30𝑥 divided by 30 is equal to 𝑥. Therefore, 𝑥 is greater than 1710 divided by 30. As this is a calculator paper, we can type this calculation into our calculator. 1710 divided by 30 is equal to 57. Therefore, 𝑥 must be greater than 57.

If, however, this calculation was on a non-calculator paper, we could divide 1710 by 30 by firstly dividing the numerator and denominator by 10. This would leave us with 171 divided by three. We could work this out using the bus stop method. 17 divided by three is equal to five remainder two. And 21 divided by three is equal to seven. Therefore, 171 divided by three is equal to 57.

If a company has revenue of 45𝑥 and cost of 15𝑥 plus 1710, they must produce more than 57 units to make a profit. The correct answer was option A) 𝑥 is greater than 57.

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