Question

Your school is donating items to the local food pantry. Your homeroom is having a competition to see who will donate the most items. You have already donated 14 items and plan to donate 3 more each week. Your friend has already collected 8 items and plans to collect 5 more items each week. Write and solve a system of equations for the number of weeks (x) when you both donate the same number of items (y).

Answer 1

First equation: y = 14 + 3x

Second equation: y = 8 + 5x

Explanation:

To model this situation, we can set up a system of two equations. The first equation will represent the number of items you have collected after a certain number of weeks, and the second equation will represent the number of items your friend has collected after the same number of weeks.

First equation: y = 14 + 3x

Second equation: y = 8 + 5x

To find the number of weeks it takes for you both to donate the same number of items, we can set the two equations equal to each other and solve for x.

14 + 3x = 8 + 5x

6x = 6

x = 1

It will take 1 week for you both to donate the same number of items. To find the total number of items each of you will have donated at that point, we can substitute 1 for x in either of the original equations and solve for y.

For example, substituting 1 for x in the first equation gives us: y = 14 + 3(1) = 14 + 3 = 17

So, after 1 week, you will have donated 17 items, and your friend will have donated the same number of items.

Answer 2

Answer: It will take 3 weeks for both of us to have collected the same

Step-by-step explanation: just did this