PSLE
Owen packed 460 croissants into large and small boxes. He filled each large box with 14 croissants and each small box with 6 croissants. All the boxes were full and no croissants were left over. What was the least number of boxes used by Owen?
To have the least number of boxes, Owen had to use as many as large boxes as possible.

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

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

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

Number of small boxes needed to pack 26 croissants
= 26 ÷ 6
= 4 r 2 (x)

There should be no remaining croissants left. So, Owen had to use less large boxes.

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

Number of small boxes to pack 40 croissants
= 40 ÷ 6
= 6 r 4 (x)

There should be no remaining croissants left. So, Owen had to use less large boxes.

If Owen used 29 large boxes,
number of croissants to be packed in small boxes
= 460 - (29 x 14)
= 460 - 406
= 54

Number of small boxes to pack 54 croissants
= 54 ÷ 6
= 9 r 0 (✓) There is no remaining croissants left.

Least number of boxes that Owen used
= 29 + 9
= 38

Answer(s): 38