PSLE
Caden packed 408 scones into large and small boxes. He filled each large box with 18 scones and each small box with 4 scones. All the boxes were full and no scones were left over. What was the least number of boxes used by Caden?
To have the least number of boxes, Caden had to use as many as large boxes as possible.

If Caden used only large boxes,
number of large boxes used
= 408 ÷ 18
= 22 r 12 (x) There should be no remaining scones left.

If 22 large boxes are used, there are 12 scones left, Caden had to use less large boxes so that the rest of the scones were packed in small boxes.

If Caden used 21 large boxes,
number of scones to be packed in small boxes
= 408 - (21 x 18)
= 408 - 378
= 30

Number of small boxes needed to pack 30 scones
= 30 ÷ 4
= 7 r 2 (x)

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

If Caden used 20 large boxes,
number of scones to be packed in small boxes
= 408 - (20 x 18)
= 408 - 360
= 48

Number of small boxes to pack 48 scones
= 48 ÷ 4
= 12 r 0 (✓) There is no remaining scones left.

Least number of boxes that Caden used
= 20 + 12
= 32

Answer(s): 32