lesson 1: relationships between quantities\ncool down: movie theater popcorn, revisited\na movie theater…

lesson 1: relationships between quantities\ncool down: movie theater popcorn, revisited\na movie theater sells popcorn in bags of different sizes. the table shows the volume of popcorn and the price of the bag.\nvolume of popcorn (ounces) price of bag ($)\n10 6\n20 8\n35 11\n48 13.6\nif the theater wanted to offer a 60-ounce bag of popcorn, what would be a good price? explain your reasoning.

lesson 1: relationships between quantities\ncool down: movie theater popcorn, revisited\na movie theater sells popcorn in bags of different sizes. the table shows the volume of popcorn and the price of the bag.\nvolume of popcorn (ounces) price of bag ($)\n10 6\n20 8\n35 11\n48 13.6\nif the theater wanted to offer a 60-ounce bag of popcorn, what would be a good price? explain your reasoning.

Answer

Explanation:

Step1: Identify linear relationship

We first assume the relationship between volume (x) (ounces) and price (y) ($) is linear, in the form (y = mx + b). Take two points ((10,6)) and ((20,8)): Calculate slope (m=\frac{8-6}{20-10}=\frac{2}{10}=0.2)

Step2: Find y-intercept (b)

Substitute (x=10,y=6,m=0.2) into (y=mx+b): (6=0.2\times10 + b) (6=2 + b) (b=6-2=4) So the linear model is (y=0.2x + 4)

Step3: Verify the model

Check with (x=35): (y=0.2\times35+4=7+4=11), matches the table. Check with (x=48): (y=0.2\times48+4=9.6+4=13.6), matches the table.

Step4: Calculate price for 60 ounces

Substitute (x=60) into (y=0.2x + 4): (y=0.2\times60+4=12+4=16)

Answer:

A good price for a 60-ounce bag of popcorn would be $16. The relationship between volume and price is linear, with the equation (y=0.2x + 4) (where (x) is volume in ounces and (y) is price in dollars), which perfectly fits the given data points. Using this model, the price for 60 ounces is calculated to be $16.