SAT question 4fe4fd7c (Linear Functions)

Question

c(x) = mx + 500 A company's total cost c(x) , in dollars, to produce x shirts is given by the function above, where m is a constant and x > 0 . The total cost to produce 100 shirts is $ 800 . What is the total cost, in dollars, to produce 1,000 shirts? (Disregard the $ sign when gridding your answer.)

College Board · Accepted Answer

The correct answer is 3500. The correct answer is 3500 . The given information includes a cost, $ 800 , to produce 100 shirts. Substituting c(x) = 800 and x = 100 into the given equation yields 800 = m × 100 + 500 . Subtracting 500 from both sides of the equation yields 300 = m × 100 . Dividing both sides of this equation by 100 yields 3 = m . Substituting the value of m into the given equation yields c(x) = 3x + 500 . Substituting 1,000 for x in this equation and solving for c(x) gives the cost of 1,000 shirts: 3 × 1,000 + 500 , or 3,500 .

CookSAT · Answer

Note: Use regression to solve for m from the given point, and evaluate the cost for 1,000 shirts.

Explanation

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SAT Question 4fe4fd7c: Linear Functions answer and explanation with Desmos solution

Explanation

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