PSLE
Gabriel packed 404 croissants into large and small boxes. He filled each large box with 10 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 Gabriel?
To have the least number of boxes, Gabriel had to use as many as large boxes as possible.

If Gabriel used only large boxes,
number of large boxes used
= 404 ÷ 10
= 40 r 4 (x) There should be no remaining croissants left.

If 40 large boxes are used, there are 4 croissants left, Gabriel had to use less large boxes so that the rest of the croissants were packed in small boxes.

If Gabriel used 39 large boxes,
number of croissants to be packed in small boxes
= 404 - (39 x 10)
= 404 - 390
= 14

Number of small boxes needed to pack 14 croissants
= 14 ÷ 8
= 1 r 6 (x)

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

If Gabriel used 38 large boxes,
number of croissants to be packed in small boxes
= 404 - (38 x 10)
= 404 - 380
= 24

Number of small boxes to pack 24 croissants
= 24 ÷ 8
= 3 r 0 (✓) There is no remaining croissants left.

Least number of boxes that Gabriel used
= 38 + 3
= 41

Answer(s): 41