PSLE
Warren packed 476 biscuits into large and small boxes. He filled each large box with 16 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 Warren?
To have the least number of boxes, Warren had to use as many as large boxes as possible.

If Warren used only large boxes,
number of large boxes used
= 476 ÷ 16
= 29 r 12 (x) There should be no remaining biscuits left.

If 29 large boxes are used, there are 12 biscuits left, Warren had to use less large boxes so that the rest of the biscuits were packed in small boxes.

If Warren used 28 large boxes,
number of biscuits to be packed in small boxes
= 476 - (28 x 16)
= 476 - 448
= 28

Number of small boxes needed to pack 28 biscuits
= 28 ÷ 6
= 4 r 4 (x)

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

If Warren used 27 large boxes,
number of biscuits to be packed in small boxes
= 476 - (27 x 16)
= 476 - 432
= 44

Number of small boxes to pack 44 biscuits
= 44 ÷ 6
= 7 r 2 (x)

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

If Warren used 26 large boxes,
number of biscuits to be packed in small boxes
= 476 - (26 x 16)
= 476 - 416
= 60

Number of small boxes to pack 60 biscuits
= 60 ÷ 6
= 10 r 0 (✓) There is no remaining biscuits left.

Least number of boxes that Warren used
= 26 + 10
= 36

Answer(s): 36