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 30 cm. The height of the space in the shelf is 78 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 = 30  --- (2)

(1) - (2)
(6 L + 2 H) - (3 L + 2 H) = 42 - 30
3 L = 12
1 L = 12 ÷ 3 = 4

From (2)
1 H
= (30 - 12) ÷ 2
= 18 ÷ 2
= 9 cm

Number of lengths to stack excluding one glass
= (78 - 9) ÷ 4
= 69 ÷ 4
= 17 r 1

Maximum number of glasses that can be stacked
= 17 + 1
= 18

Answer(s): 18