PSLE
Owen packed 312 wafers into large and small boxes. He filled each large box with 14 wafers and each small box with 4 wafers. All the boxes were full and no wafers were left over. What was the least number of boxes used by Owen?
To have the least number of boxes, Owen had to use as many as large boxes as possible.

If Owen used only large boxes,
number of large boxes used
= 312 ÷ 14
= 22 r 4 (x) There should be no remaining wafers left.

If 22 large boxes are used, there are 4 wafers left, Owen had to use less large boxes so that the rest of the wafers were packed in small boxes.

If Owen used 21 large boxes,
number of wafers to be packed in small boxes
= 312 - (21 x 14)
= 312 - 294
= 18

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

There should be no remaining wafers left. So, Owen had to use less large boxes.

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

Number of small boxes to pack 32 wafers
= 32 ÷ 4
= 8 r 0 (✓) There is no remaining wafers left.

Least number of boxes that Owen used
= 20 + 8
= 28

Answer(s): 28