PSLE
Valen packed 268 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 Valen?
To have the least number of boxes, Valen had to use as many as large boxes as possible.

If Valen used only large boxes,
number of large boxes used
= 268 ÷ 14
= 19 r 2 (x) There should be no remaining croissants left.

If 19 large boxes are used, there are 2 croissants left, Valen had to use less large boxes so that the rest of the croissants were packed in small boxes.

If Valen used 18 large boxes,
number of croissants to be packed in small boxes
= 268 - (18 x 14)
= 268 - 252
= 16

Number of small boxes needed to pack 16 croissants
= 16 ÷ 6
= 2 r 4 (x)

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

If Valen used 17 large boxes,
number of croissants to be packed in small boxes
= 268 - (17 x 14)
= 268 - 238
= 30

Number of small boxes to pack 30 croissants
= 30 ÷ 6
= 5 r 0 (✓) There is no remaining croissants left.

Least number of boxes that Valen used
= 17 + 5
= 22

Answer(s): 22