PSLE
Tommy packed 312 biscuits into large and small boxes. He filled each large box with 20 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 Tommy?
To have the least number of boxes, Tommy had to use as many as large boxes as possible.

If Tommy used only large boxes,
number of large boxes used
= 312 ÷ 20
= 15 r 12 (x) There should be no remaining biscuits left.

If 15 large boxes are used, there are 12 biscuits left, Tommy had to use less large boxes so that the rest of the biscuits were packed in small boxes.

If Tommy used 14 large boxes,
number of biscuits to be packed in small boxes
= 312 - (14 x 20)
= 312 - 280
= 32

Number of small boxes needed to pack 32 biscuits
= 32 ÷ 6
= 5 r 2 (x)

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

If Tommy used 13 large boxes,
number of biscuits to be packed in small boxes
= 312 - (13 x 20)
= 312 - 260
= 52

Number of small boxes to pack 52 biscuits
= 52 ÷ 6
= 8 r 4 (x)

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

If Tommy used 12 large boxes,
number of biscuits to be packed in small boxes
= 312 - (12 x 20)
= 312 - 240
= 72

Number of small boxes to pack 72 biscuits
= 72 ÷ 6
= 12 r 0 (✓) There is no remaining biscuits left.

Least number of boxes that Tommy used
= 12 + 12
= 24

Answer(s): 24