Cari Bean was on her way to the islands in her yachet. Because of the waves and the currents, she was making irregular progess. The first day she traveled 100 miles. The second day she traversed 120 miles, and the third day only 90 miles. On the fourth day she made 110 miles, and on the fifth day, 80 miles. If this trend continues, how many miles will she have traveled in ten days?

I don't see much of a trend. In five days, she has gone 500 miles.

At that overall rate, she will have gone 1000 miles in 10 days.

On the other hand, her differences from day to day have been +20 -30 +20 -30. If that pattern continues, she'll have gone 100+ [800+4(-10)] + [100+20] = 980 miles.

To find out how many miles Cari will have traveled in ten days, we need to observe the given information and look for a pattern in her daily progress.

We can see that the pattern of her daily progress is irregular, but we can still identify a common trend. Let's calculate the average distance Cari traveled on each day:

Average Distance = (Sum of Distances) / (Number of Days)

On the first day, Cari traveled 100 miles.
On the second day, Cari traveled 120 miles.
On the third day, Cari traveled 90 miles.
On the fourth day, Cari traveled 110 miles.
On the fifth day, Cari traveled 80 miles.

Sum of distances = 100 + 120 + 90 + 110 + 80 = 500 miles
Number of days = 5

Average Distance = 500 miles / 5 days = 100 miles per day

Based on this average, we can assume that Cari will continue to travel 100 miles per day in the following days. So, to find out how many miles she will have traveled in ten days, we can multiply the average distance per day by the number of days:

Distance traveled in 10 days = 100 miles/day * 10 days = 1000 miles

Therefore, if the trend continues, Cari will have traveled 1000 miles in ten days.