6 equal cups stacked together, have a hight of 19.45 cm. The same cup, 3 cups stacked together have a hight of 13.51 cm. What is the hight of 1 cup?

Question

I found this in my tution practice paper. 

 

Answer 1

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

-------------------

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!