Need help with a word problem - Carrie collected can food for a homeless shelter each day for one week. On day one she collected 7 cans, on day two she collected 8 cans, on day three she collected 10 cans and on day four she collected 13 cans. If Carrie wanted to give at least 100 cans of food to the shelter and this pattern of can collecting continued, did she meet her goal?

Day Cans

1-----7
2-----8
3-----10
4-----13
5-----17
6-----22
7-----28

Total-105.

To determine whether Carrie met her goal of collecting at least 100 cans of food for the homeless shelter, we need to find out how many cans she collected in total.

Given that Carrie collected cans for one week, we can assume that she collected cans for seven consecutive days. To calculate the total number of cans collected, we can add up the number of cans collected each day.

Day one: 7 cans
Day two: 8 cans
Day three: 10 cans
Day four: 13 cans

To find out the total number of cans collected, we sum up the cans collected each day:

7 + 8 + 10 + 13

Calculating this sum, we get:

38 cans

So, Carrie collected 38 cans in the first four days. Now, let's see if this pattern continues.

Since the question does not provide information about the number of cans collected on the remaining three days, we can assume that the pattern continued. This means we will continue to add cans to the total for the remaining three days.

To determine the total number of cans collected, we add the number of cans collected in the first four days, to the number of cans collected in the remaining three days:

38 + x + y + z

Let's assume that on the remaining three days, Carrie collected a constant number of cans each day. Since we need to meet a goal of at least 100 cans, we can set up the following equation:

38 + x + y + z ≥ 100

Now, we can solve for the minimum number of cans (x + y + z) needed on the remaining three days:

x + y + z ≥ 100 - 38
x + y + z ≥ 62

By solving this inequality, we can determine whether Carrie met her goal by collecting at least 100 cans for the homeless shelter.