PSLE
The figure shows two stacks of identical paper cups. There are 6 cups in the shorter stack and 10 cups in the longer one. The length of the shorter stack is 23 cm and the length of the longer stack is 31 cm. Mark wants to pack the paper cups as a single stack into a box ³₄ m long. What is the most number of paper cups he can pack into the box?
Difference in the height of paper cups between the shorter and the longer stack
= 31 - 23
= 8 cm

Difference in the number of paper cups between the shorter and the longer stack
= 10 - 6
= 4

Height of each increment
= 8 ÷ 4
= 2 cm

Number of increments in the shorter stack
= 6 - 1
= 5

Height of each paper cup
= 23 - (5 x 2)
= 23 - 10
= 13 cm

1 m = 100 cm

³₄ m = ³₄ x 100 = 75 cm

Number of height increments that he can pack into the box
= (75 - 13) ÷ 2
= 62 ÷ 2
= 31 r 0

Number of paper cups stacked on top of the first one = 31

Most number of paper cups he can pack into the box including the first one
= 31 + 1
= 32

Answer(s): 32