Question

some identical glasses are stacked on top of each other. a stack with eight glasses is 42 cm high. a stack with two glasses is 18 cm high. how high is a stack with six glasses?

Answer 1

34 cm

Explanation:

You want the height of a stack of 6 identical glasses if a stack of 2 is 18 cm high, and a stack of 8 is 42 cm high.

Linear relation

We assume the stacks of glasses are constructed on some base, accounting for the fact that the height is not proportional to the number of glasses. We can find the slope of the relation using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (42 -18)/(8 -2) = 24/6 = 4

Then the relation can be written in point-slope form as ...

y -k = m(x -h) . . . . . . slope m through point (h, k)

y -18 = 4(x -2)

6 glasses

For x = 6, the value of y is ...

y -18 = 4(6 -2)

y = 16 +18 = 34 . . . . . add 18

A stack of 6 glasses is 34 cm high.

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Additional comment

The base is 10 cm high, and each glass is 4 cm high.

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