Question

An international food festival charges for admission and for each sample of food. Admission and 7 samples cost ​$11.25. Admission and 9 samples cost $13.25. Write a linear function rule to model the cost y for any number of samples x.

Answer 1

y = x + 4.25

Explanation:

Let

y = total cost

x = cost of food sample

b = cost of admission

y = mx + b

Sample 1:

y = mx + b

11.25 = m*7 + b

11.25 = 7m + b

Sample 2:

y = mx + b

13.25 = m*9 + b

13.25 = 9m + b

Solve the equations simultaneously

11.25 = 7m + b (1)

13.25 = 9m + b (2)

Multiply (1) by 9 and (2) by 7

101.25 = 63m + 9b

92.75 = 63m + 7b

Subtract

101.25 - 92.75 = 9b - 7b

8.5 = 2b

b = 8.5/2

= 4.25

b = 4.25

Substitute b = 4.25 into (1)

11.25 = 7m + b (1)

11.25 = 7m + 4.25

11.25 - 4.25 = 7m

7 = 7m

m = 7/7

= 1

m = 1

y = mx + b

y = x + 4.25