Question Video: Evaluating a Linear Function by Direct Substitution

A company produces greeting cards with an initial cost of 2000 LE and an extra cost of 1/2 LE per card. The total cost is given by 𝐶 = (1/2)𝑥 + 2000, where 𝑥 is the number of produced cards. Find the total cost of producing 15,000 cards.

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Video Transcript

A company produces greeting cards with an initial cost of 2,000 Egyptian pounds and an extra cost of half an Egyptian pound per card. The total cost is given by 𝐶 is equal to a half 𝑥 plus 2,000, where 𝑥 is the number of produced cards. Find the total cost of producing 15,000 cards.

In this question, we are given a formula for the total cost. 𝐶 is equal to a half 𝑥 plus 2,000. As 𝑥 is the number of cards produced, we can substitute any value of 𝑥 into the formula to calculate the total cost. In this question, we are told that 𝑥 is equal to 15,000. Substituting in this value gives us 𝐶 is equal to a half multiplied by 15,000 plus 2,000. One-half multiplied by 15 or a half of 15 is 7.5. This means that a half multiplied by 15,000 is 7,500. 𝐶 is equal to 7,500 plus 2,000. This is equal to 9,500. The total cost of producing 15,000 cards is 9,500 Egyptian pounds.

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