PSLE
Fabian packed 452 croissants into large and small boxes. He filled each large box with 14 croissants and each small box with 8 croissants. All the boxes were full and no croissants were left over. What was the least number of boxes used by Fabian?
To have the least number of boxes, Fabian had to use as many as large boxes as possible.

If Fabian used only large boxes,
number of large boxes used
= 452 ÷ 14
= 32 r 4 (x) There should be no remaining croissants left.

If 32 large boxes are used, there are 4 croissants left, Fabian had to use less large boxes so that the rest of the croissants were packed in small boxes.

If Fabian used 31 large boxes,
number of croissants to be packed in small boxes
= 452 - (31 x 14)
= 452 - 434
= 18

Number of small boxes needed to pack 18 croissants
= 18 ÷ 8
= 2 r 2 (x)

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

If Fabian used 30 large boxes,
number of croissants to be packed in small boxes
= 452 - (30 x 14)
= 452 - 420
= 32

Number of small boxes to pack 32 croissants
= 32 ÷ 8
= 4 r 0 (✓) There is no remaining croissants left.

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

Answer(s): 34