PSLE
Ben packed 438 biscuits into large and small boxes. He filled each large box with 10 biscuits and each small box with 4 biscuits. All the boxes were full and no biscuits were left over. What was the least number of boxes used by Ben?
To have the least number of boxes, Ben had to use as many as large boxes as possible.

If Ben used only large boxes,
number of large boxes used
= 438 ÷ 10
= 43 r 8 (x) There should be no remaining biscuits left.

If 43 large boxes are used, there are 8 biscuits left, Ben had to use less large boxes so that the rest of the biscuits were packed in small boxes.

If Ben used 42 large boxes,
number of biscuits to be packed in small boxes
= 438 - (42 x 10)
= 438 - 420
= 18

Number of small boxes needed to pack 18 biscuits
= 18 ÷ 4
= 4 r 2 (x)

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

If Ben used 41 large boxes,
number of biscuits to be packed in small boxes
= 438 - (41 x 10)
= 438 - 410
= 28

Number of small boxes to pack 28 biscuits
= 28 ÷ 4
= 7 r 0 (✓) There is no remaining biscuits left.

Least number of boxes that Ben used
= 41 + 7
= 48

Answer(s): 48