Question

The environment club has saved 200 pounds of cans and promises to collect 20 pounds of cans each week and will use the profits to buy additional recycling bins. Create a linear model for their collection program. When will the club have 320 pounds of cans?

Answer 1

The linear model for the collection program is y = 20x + 200. The club will have 320 pounds of cans after 6 weeks.

Step-by-step explanation:

To create a linear model for the collection program, we can use the equation y = mx + b, where y represents the total weight of cans collected, x represents the number of weeks, m represents the rate at which cans are collected each week, and b represents the initial number of pounds of cans saved by the environment club. In this case, m = 20 (since they promise to collect 20 pounds of cans each week) and b = 200 (since they have already saved 200 pounds of cans). So, the linear model for the collection program is y = 20x + 200.

To determine when the club will have 320 pounds of cans, we can substitute y = 320 into the equation and solve for x: 320 = 20x + 200. Subtracting 200 from both sides, we get 120 = 20x. Dividing both sides by 20, we find x = 6. Therefore, the club will have 320 pounds of cans after 6 weeks.