The figure shows two stacks of identical glasses. The height of the first stack of 8 glasses is 40 cm. The height of the second stack of 5 glasses is 25 cm. The height of the space in the shelf is 72 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 = 40  --- (1)
3 L + 2 H = 25  --- (2)

(1) - (2)
(6 L + 2 H) - (3 L + 2 H) = 40 - 25
3 L = 15
1 L = 15 ÷ 3 = 5

From (2)
1 H
= (25 - 15) ÷ 2
= 10 ÷ 2
= 5 cm

Number of lengths to stack excluding one glass
= (72 - 5) ÷ 5
= 67 ÷ 5
= 13 r 2

Maximum number of glasses that can be stacked
= 13 + 1
= 14

Answer(s): 14