Jackson went into a movie theater and bought 8 bags of popcorn (x) and 2 candies (y), costing a total of $58. Cooper went into the same movie theater and bought 4 bags of popcorn (x) and 5 candies (y), costing a total of $49. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each candy. What is the price of 1 bag of popcorn and 1 candy?

(a)

(b)

Bag of popcorn = $6

Candy = $5

Step-by-step explanation:

Given

Jackson: x = 8; y= 2; Total = 58

Cooper: x = 4; y= 5; Total = 49

Solving (a): System of equation

For Jackson:

This is done by multiplying each variable by the quantity.

Same will be applied to Cooper's purchase:

Cooper:

Solving (b): Price of 1 bag of popcorn and 1 candy

This implies that we solve for x and y

----- (1)

-------- (2)

Multiply the second equation by 2

-------- (3)

Subtract the (1) from (3)

Solve for y

Substitute 5 for y in (1)

Solve for x

This implies:

Bag of popcorn = $6

Candy = $5

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).