PSLE
David packed 432 scones into large and small boxes. He filled each large box with 14 scones and each small box with 10 scones. All the boxes were full and no scones were left over. What was the least number of boxes used by David?
To have the least number of boxes, David had to use as many as large boxes as possible.

If David used only large boxes,
number of large boxes used
= 432 ÷ 14
= 30 r 12 (x) There should be no remaining scones left.

If 30 large boxes are used, there are 12 scones left, David had to use less large boxes so that the rest of the scones were packed in small boxes.

If David used 29 large boxes,
number of scones to be packed in small boxes
= 432 - (29 x 14)
= 432 - 406
= 26

Number of small boxes needed to pack 26 scones
= 26 ÷ 10
= 2 r 6 (x)

There should be no remaining scones left. So, David had to use less large boxes.

If David used 28 large boxes,
number of scones to be packed in small boxes
= 432 - (28 x 14)
= 432 - 392
= 40

Number of small boxes to pack 40 scones
= 40 ÷ 10
= 4 r 0 (✓) There is no remaining scones left.

Least number of boxes that David used
= 28 + 4
= 32

Answer(s): 32