Question

Nori and Mason are participating in a recycling challenge. Nori has 14 pounds of aluminum cans and set a goal to collect 3 more pounds each week. Mason has 6 pounds of aluminum cans and set a goal to collect 4 more pounds each week. If they meet their goals, in how many weeks will Nori and Mason have collected the same amount of aluminum cans?

Answer 1

Using linear equations, it's shown that Nori and Mason will have collected the same amount of aluminum cans after 8 weeks.

Step-by-step explanation:

To find out in how many weeks Nori and Mason will have collected the same amount of aluminum cans, we can set up a linear equation for each person and then solve for the point where they intersect, as that will tell us when they have the same amount. We'll let w represent the number of weeks.

Nori starts with 14 pounds and collects 3 more pounds each week, so Nori's total after w weeks is 14 + 3w. Mason starts with 6 pounds and collects 4 more pounds each week, making Mason's total after w weeks 6 + 4w.

Setting the two expressions equal to each other to find the week they will have the same amount gives us:
14 + 3w = 6 + 4w
Solving for w we subtract 3w from both sides and subtract 6 from both sides to isolate w:
14 - 6 = 4w - 3w
8 = w

So, Nori and Mason will have collected the same amount of aluminum cans after 8 weeks.