SAT Math Multiple Choice Question 546: Answer and Explanation

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Question: 546

6.

The graph shows the average cost of back surgery followed by a hospital stay in the United States. The hospital charges for the surgery itself plus all the costs associated with recovery care for each night the patient remains in the hospital. Based on the graph, what is the average cost per night spent in the hospital?

  • A. $2,600
  • B. $4,000
  • C. $6,600
  • D. $8,000

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: In a real-world scenario, the slope of a line represents a unit rate and the y-intercept represents a flat fee or a starting amount.

Getting to the Answer: The cost per night in the hospital is the same as the unit rate, which is represented by the slope of the line. Use the grid-lines and the axis labels to count the rise and the run from the y-intercept of the line (0, 26,000) to the next point that hits an intersection of two grid-lines (2, 34,000). Pay careful attention to how the grid-lines are marked (by 2s on the x-axis and by 2,000s on the y-axis). The line rises 8,000 units and runs 2 units, so the slope is which means it costs an average of $4,000 per night to stay in the hospital. Note that you could also use the slope formula and the two points to find the slope:

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