PSLE
Owen packed 474 biscuits into large and small boxes. He filled each large box with 12 biscuits and each small box with 10 biscuits. All the boxes were full and no biscuits were left over. What was the least number of boxes used by Owen?
To have the least number of boxes, Owen had to use as many as large boxes as possible.

If Owen used only large boxes,
number of large boxes used
= 474 ÷ 12
= 39 r 6 (x) There should be no remaining biscuits left.

If 39 large boxes are used, there are 6 biscuits left, Owen had to use less large boxes so that the rest of the biscuits were packed in small boxes.

If Owen used 38 large boxes,
number of biscuits to be packed in small boxes
= 474 - (38 x 12)
= 474 - 456
= 18

Number of small boxes needed to pack 18 biscuits
= 18 ÷ 10
= 1 r 8 (x)

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

If Owen used 37 large boxes,
number of biscuits to be packed in small boxes
= 474 - (37 x 12)
= 474 - 444
= 30

Number of small boxes to pack 30 biscuits
= 30 ÷ 10
= 3 r 0 (✓) There is no remaining biscuits left.

Least number of boxes that Owen used
= 37 + 3
= 40

Answer(s): 40