PSLE
Zeph packed 230 puffs into large and small boxes. He filled each large box with 14 puffs and each small box with 6 puffs. All the boxes were full and no puffs were left over. What was the least number of boxes used by Zeph?
To have the least number of boxes, Zeph had to use as many as large boxes as possible.

If Zeph used only large boxes,
number of large boxes used
= 230 ÷ 14
= 16 r 6 (x) There should be no remaining puffs left.

If 16 large boxes are used, there are 6 puffs left, Zeph had to use less large boxes so that the rest of the puffs were packed in small boxes.

If Zeph used 15 large boxes,
number of puffs to be packed in small boxes
= 230 - (15 x 14)
= 230 - 210
= 20

Number of small boxes needed to pack 20 puffs
= 20 ÷ 6
= 3 r 2 (x)

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

If Zeph used 14 large boxes,
number of puffs to be packed in small boxes
= 230 - (14 x 14)
= 230 - 196
= 34

Number of small boxes to pack 34 puffs
= 34 ÷ 6
= 5 r 4 (x)

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

If Zeph used 13 large boxes,
number of puffs to be packed in small boxes
= 230 - (13 x 14)
= 230 - 182
= 48

Number of small boxes to pack 48 puffs
= 48 ÷ 6
= 8 r 0 (✓) There is no remaining puffs left.

Least number of boxes that Zeph used
= 13 + 8
= 21

Answer(s): 21