PSLE
Liam packed 286 croissants into large and small boxes. He filled each large box with 14 croissants and each small box with 12 croissants. All the boxes were full and no croissants were left over. What was the least number of boxes used by Liam?
To have the least number of boxes, Liam had to use as many as large boxes as possible.

If Liam used only large boxes,
number of large boxes used
= 286 ÷ 14
= 20 r 6 (x) There should be no remaining croissants left.

If 20 large boxes are used, there are 6 croissants left, Liam had to use less large boxes so that the rest of the croissants were packed in small boxes.

If Liam used 19 large boxes,
number of croissants to be packed in small boxes
= 286 - (19 x 14)
= 286 - 266
= 20

Number of small boxes needed to pack 20 croissants
= 20 ÷ 12
= 1 r 8 (x)

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

If Liam used 18 large boxes,
number of croissants to be packed in small boxes
= 286 - (18 x 14)
= 286 - 252
= 34

Number of small boxes to pack 34 croissants
= 34 ÷ 12
= 2 r 10 (x)

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

If Liam used 17 large boxes,
number of croissants to be packed in small boxes
= 286 - (17 x 14)
= 286 - 238
= 48

Number of small boxes to pack 48 croissants
= 48 ÷ 12
= 4 r 0 (✓) There is no remaining croissants left.

Least number of boxes that Liam used
= 17 + 4
= 21

Answer(s): 21