Every week Sarah collects a few pounds of cans to recycle. The graph below shows the total number of pounds of cans (y) that Sarah collected in a certain amount of time (x), in weeks:

Question

A graph titled Can Recycling is shown with labels in x axis and y axis as Number of Weeks and Amount of Cans Collected in pounds, respectively. The values on the x axis are from 0 to 5 at increments of 1, and the values on the y axis are from 0 to 100 with increments of 20. Dots are made at 0, 20 and 1, 40 and 2, 60 and 3, 80 and 4, 100. A straight line joins the ordered pairs 0, 20 and 4,100.
What would most likely be the total amount of cans, in pounds, Sarah would collect in 10 weeks? (5 points)

A: 200

B: 220

C: 320

D: 420

Answer 1

Since the ordered pairs on the line are 0, 20 and 4, 100, we can find the rate at which the amount of cans collected is increasing.

First, we find the slope of the line:
Slope = (Change in y)/(Change in x) = (100 - 20)/(4 - 0) = 80/4 = 20

So, for every 1 week, Sarah collects 20 pounds of cans.

To find the total amount of cans she would collect in 10 weeks, we can multiply the slope by 10:
20 pounds/week * 10 weeks = 200 pounds

Therefore, the most likely total amount of cans Sarah would collect in 10 weeks is 200 pounds, which is option A.