PSLE
Mark packed 460 puffs into large and small boxes. He filled each large box with 14 puffs and each small box with 10 puffs. All the boxes were full and no puffs were left over. What was the least number of boxes used by Mark?
To have the least number of boxes, Mark had to use as many as large boxes as possible.

If Mark used only large boxes,
number of large boxes used
= 460 ÷ 14
= 32 r 12 (x) There should be no remaining puffs left.

If 32 large boxes are used, there are 12 puffs left, Mark had to use less large boxes so that the rest of the puffs were packed in small boxes.

If Mark used 31 large boxes,
number of puffs to be packed in small boxes
= 460 - (31 x 14)
= 460 - 434
= 26

Number of small boxes needed to pack 26 puffs
= 26 ÷ 10
= 2 r 6 (x)

There should be no remaining puffs left. So, Mark had to use less large boxes.

If Mark used 30 large boxes,
number of puffs to be packed in small boxes
= 460 - (30 x 14)
= 460 - 420
= 40

Number of small boxes to pack 40 puffs
= 40 ÷ 10
= 4 r 0 (✓) There is no remaining puffs left.

Least number of boxes that Mark used
= 30 + 4
= 34

Answer(s): 34