In a dorm meal plan you pay a membership fee; then all your meals are at a fixed price per meal. a. If 100 meals cost $1125 and 160 meals cost $1440, write a linear function that describes the cost of a meal plan, c, in terms of the number of meals, n. Write your equation in slope-intercept form.
b. What is the cost of each meal and what is the membership fee.
c. Find the cost of 140 meals.
I'm totally lost on this one.

9514 1404 393

Step-by-step explanation:

a. Using the variables defined for you, there are two points given:

  (n, c) = (100, 1125) and (160, 1440)

You can use the 2-point form of the equation for a line to find the desired linear function:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . when given points (x1, y1), (x2, y2)

  c = (1440 -1125)/(160 -100)(n -100) +1125 . . . fill in given values

  c = 315/60(n -100) +1125

  c = 5.25n +600

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b. The cost of each meal is the amount by which the total cost goes up when the number of meals goes up by 1. That is the coefficient of n, 5.25. The membership fee is the cost of 0 meals, 600.

The cost of each meal is $5.25; the membership fee is $600.

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c. For n = 140, the cost is ...

  c = 5.25(140) +600 = 735 +600 = 1335

The cost of 140 meals is $1335.