In a college meal plan you pay a membership fee then all of

In a college meal plan you pay a membership fee, then all of your meals are at a fixed price per week. If 30 meals cost $152.5 and 70 meals cost $252.5, answer the following questions: Write a formula for the cost of a meal plan. C, in terms of the number of meals, n. C = What is the membership fee? What is the price per meal? Find the cost for 50 meals. Find n in terms of C. n = Finally, use your answer in part (e) to determine the maximum number of meals you can buy on a budget of $300. Maximum number of meals implies if you find that n = 3.9, then you can buy a maximum of 3 meals. You must truncate any decimal solutions (which is different from rounding). n =

Solution

( 30 meals , $ 152.5 ) ( 70 meals , $ 252.5)

slope = ( 252.5 - 152.5)/(70 - 30) = 100/40 2.5 $ /meal

C(n) = mn + p ; find p

152.5 = 2.5*30 + p ; p = 77.5

C(n) = 2.5n + 77.5

Member ship fee is $ 77.5 ie.e fixed cost

Price per meal = slope = $ 2.5

Cost of 50 meals : C(50) = 2.5*50 + 77.5 = $ 202.5

Find n in terms of C : C(n) = 2.5n + 77.5

n = ( C - 77.5)/2.5