Video: Solving Word Problems Involving Arithmetic Sequences

A man works in a grocery store. He stacks tuna cans in rows, where there are 39 cans in the first row, 37 in the second, 35 in the third, and so on. Find the row which has exactly 29.

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Video Transcript

A man works in a grocery store. He stacks tuna cans in rows, where there are 39 cans in the first row, 37 in the second, 35 in the third, and so on. Find the row which has exactly 29.

In row number one, there are 39 cans. In row number two, there are 37. In row number three, there are 35. And this pattern continues. We recognize that each row has two less cans than the previous row. One way to solve this problem would be to continue to subtract two. Row four would be 35 minus two, which is 33. 33 minus two is 31. So the fifth row would have 31 cans. And 31 minus two is 29. The sixth row would have 29 cans. This tells us that row six has exactly 29 cans.

Let’s consider a second method which wouldn’t require us to list out all the rows. We know that there are 39 cans in the first row. And we want to know which row has 29 cans. To get from 39 to 29, we subtract 10. And we know that every time we go up a row, we take away two. We can divide negative 10 by negative two, which equals five. This tells us we need to take away two five times to get from 39 to 29. And since 39 is in row one, we need to go up five rows to get to row six, which will have 29 cans on it.

Both methods show that the sixth row would have exactly 29 cans.

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