PSLE
Daniel packed 370 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 Daniel?
To have the least number of boxes, Daniel had to use as many as large boxes as possible.

If Daniel used only large boxes,
number of large boxes used
= 370 ÷ 14
= 26 r 6 (x) There should be no remaining puffs left.

If 26 large boxes are used, there are 6 puffs left, Daniel had to use less large boxes so that the rest of the puffs were packed in small boxes.

If Daniel used 25 large boxes,
number of puffs to be packed in small boxes
= 370 - (25 x 14)
= 370 - 350
= 20

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

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

If Daniel used 24 large boxes,
number of puffs to be packed in small boxes
= 370 - (24 x 14)
= 370 - 336
= 34

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

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

If Daniel used 23 large boxes,
number of puffs to be packed in small boxes
= 370 - (23 x 14)
= 370 - 322
= 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 Daniel used
= 23 + 8
= 31

Answer(s): 31