PSLE
Ethan packed 386 wafers into large and small boxes. He filled each large box with 14 wafers and each small box with 6 wafers. All the boxes were full and no wafers were left over. What was the least number of boxes used by Ethan?
To have the least number of boxes, Ethan had to use as many as large boxes as possible.

If Ethan used only large boxes,
number of large boxes used
= 386 ÷ 14
= 27 r 8 (x) There should be no remaining wafers left.

If 27 large boxes are used, there are 8 wafers left, Ethan had to use less large boxes so that the rest of the wafers were packed in small boxes.

If Ethan used 26 large boxes,
number of wafers to be packed in small boxes
= 386 - (26 x 14)
= 386 - 364
= 22

Number of small boxes needed to pack 22 wafers
= 22 ÷ 6
= 3 r 4 (x)

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

If Ethan used 25 large boxes,
number of wafers to be packed in small boxes
= 386 - (25 x 14)
= 386 - 350
= 36

Number of small boxes to pack 36 wafers
= 36 ÷ 6
= 6 r 0 (✓) There is no remaining wafers left.

Least number of boxes that Ethan used
= 25 + 6
= 31

Answer(s): 31