Question

Handy Andy sells 23 oz. cans of green beans for 63 cents and 15 oz. cans for 45 cents. Assume the price varies linearly with the number of ounces.

a. Write a function to express the price in terms of the number of ounces in a can.
b. At the store, a 52 oz. can sells for $1.39. According to your model, is it overpriced or underpriced? Explain.
c. Suppose an 'individual serving' can of green beans costs $0.21. About how many ounces of green beans would you expect it to contain?
d. What is the slope in your model? What does it represent in the real world?
e. What is your y-intercept? What does it represent in the real world? Why isn't it at zero?

A. a- b-d, c-a, d-b, e-c
B. a-b, b-, c-d, d-a, e-b
C. a-c, b-d, c-a, d-, e-b
D. a-b, b-d, c-c, d-a, e-c

Answer 1

To express the price of green beans in terms of the number of ounces, you can use a linear function. The given information provides the prices for 23 oz. and 15 oz. cans. Use the slope-intercept form of a linear equation to find the slope and y-intercept.

Step-by-step explanation:

To write a linear function expressing the price in terms of the number of ounces, we need to find the slope and y-intercept. Let's use the given information to determine these values:

Price of 23 oz. can = $0.63
Price of 15 oz. can = $0.45

We can use the slope-intercept form of a linear equation, y = mx + b, where y is the price, x is the number of ounces, m is the slope, and b is the y-intercept.

1. Using the given prices, we can find the slope (m) as follows:
   m = (0.63 - 0.45) / (23 - 15)
   m = 0.18 / 8
   m = 0.0225
2. To find the y-intercept (b), we can substitute the slope (m) and any of the given prices into the equation:
   0.63 = 0.0225(23) + b
   b = 0.63 - 0.5175
   b = 0.1125

Therefore, the linear function expressing the price in terms of the number of ounces is y = 0.0225x + 0.1125.