PSLE
Ken packed 374 biscuits into large and small boxes. He filled each large box with 10 biscuits and each small box with 6 biscuits. All the boxes were full and no biscuits were left over. What was the least number of boxes used by Ken?
To have the least number of boxes, Ken had to use as many as large boxes as possible.

If Ken used only large boxes,
number of large boxes used
= 374 ÷ 10
= 37 r 4 (x) There should be no remaining biscuits left.

If 37 large boxes are used, there are 4 biscuits left, Ken had to use less large boxes so that the rest of the biscuits were packed in small boxes.

If Ken used 36 large boxes,
number of biscuits to be packed in small boxes
= 374 - (36 x 10)
= 374 - 360
= 14

Number of small boxes needed to pack 14 biscuits
= 14 ÷ 6
= 2 r 2 (x)

There should be no remaining biscuits left. So, Ken had to use less large boxes.

If Ken used 35 large boxes,
number of biscuits to be packed in small boxes
= 374 - (35 x 10)
= 374 - 350
= 24

Number of small boxes to pack 24 biscuits
= 24 ÷ 6
= 4 r 0 (✓) There is no remaining biscuits left.

Least number of boxes that Ken used
= 35 + 4
= 39

Answer(s): 39