SOLUTION: Students created a trapezoid from the cans they had collected for the food bank. There were 10 rows in the trapezoid. The bottom row had 100 cans. The 10th row has 136 cans. How

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Students created a trapezoid from the cans they had collected for the food bank. There were 10 rows in the trapezoid. The bottom row had 100 cans. The 10th row has 136 cans. How      Log On

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Question 1088070: Students created a trapezoid from the cans they had collected
for the food bank. There were 10 rows in the trapezoid. The
bottom row had 100 cans. The 10th row has 136 cans. How many
cans were in the 8th row?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Students created a trapezoid from the cans they had collected
for the food bank. There were 10 rows in the trapezoid. The
bottom row had 100 cans. The 10th row has 136 cans. How many
cans were in the 8th row?
It's an arithmetic sequence

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

Students created a trapezoid from the cans they had collected
for the food bank. There were 10 rows in the trapezoid.
n=10

The bottom row had 100 cans.
a%5B1%5D=100

The 10th row has 136 cans.
a%5B10%5D=135

Substitute n=10 in

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

a%5B10%5D=a%5B1%5D%2B%2810-1%29d

Substitute for a%5B10%5D and a%5B1%5D
and simplify:

136=100%2B%289%29d

36=9d

4=d

So each row had 4 more cans than the preceding row.

How many cans were in the 8th row?
Substitute a1 = 100, n=8, and d=4 in

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

You finish.

Edwin