Philip P. answered • 10/14/14

Effective and Patient Math Tutor

The assumption is that each cup fits partially inside of the one below it when you stack them. Let h = the full height of a cup and x = the height of the part that sticks out when you stack them (x<h). The bottom cup contributes its full height, h, and each of the rest contributes a height of

**x**to the stack.For the 6 cup stack we have:

h + 5x = 19.45

For the 3 cup stack:

h + 2x = 13.51

Subtract the second equation from the first:

h + 5x = 19.45

-h - 2x = -13.51

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0 + 3x = 5.94

**x = 1.98 cm**

To find h, the height of each cup:

h + 2x = 13.51

h + 2(1.98) = 13.51

h + 3.96 = 13.51

**h = 9.55 cm**

Check:

h + 5x = 19.45

9.55 + 5(1.98) = 19.45

9.55 + 9.9 = 19.45

19.45 = 19.45 Check!