PSLE
The figure shows two stacks of identical plastic cups. There are 7 cups in the shorter stack and 12 cups in the longer one. The length of the shorter stack is 22 cm and the length of the longer stack is 32 cm. Tom wants to pack the plastic cups as a single stack into a box ³₄ m long. What is the most number of plastic cups he can pack into the box?
Difference in the height of plastic cups between the shorter and the longer stack
= 32 - 22
= 10 cm

Difference in the number of plastic cups between the shorter and the longer stack
= 12 - 7
= 5

Height of each increment
= 10 ÷ 5
= 2 cm

Number of increments in the shorter stack
= 7 - 1
= 6

Height of each plastic cup
= 22 - (6 x 2)
= 22 - 12
= 10 cm

1 m = 100 cm

³₄ m = ³₄ x 100 = 75 cm

Number of height increments that he can pack into the box
= (75 - 10) ÷ 2
= 65 ÷ 2
= 32 r 1

Number of plastic cups stacked on top of the first one = 32

Most number of plastic cups he can pack into the box including the first one
= 32 + 1
= 33

Answer(s): 33