The figure shows two stacks of identical glasses. The height of the first stack of 8 glasses is 42 cm. The height of the second stack of 5 glasses is 24 cm. The height of the space in the shelf is 68 cm. What is the maximum number of glasses that you can put in a single stack to be placed in this shelf?
Let 1 H be the height of the glass.
Let 1 L be the length of each gap between the glasses.

6 L + 2 H = 42  --- (1)
3 L + 2 H = 24  --- (2)

(1) - (2)
(6 L + 2 H) - (3 L + 2 H) = 42 - 24
3 L = 18
1 L = 18 ÷ 3 = 6

From (2)
1 H
= (24 - 18) ÷ 2
= 6 ÷ 2
= 3 cm

Number of lengths to stack excluding one glass
= (68 - 3) ÷ 6
= 65 ÷ 6
= 10 r 5

Maximum number of glasses that can be stacked
= 10 + 1
= 11

Answer(s): 11