PSLE
Japheth packed 330 wafers into large and small boxes. He filled each large box with 12 wafers and each small box with 10 wafers. All the boxes were full and no wafers were left over. What was the least number of boxes used by Japheth?
To have the least number of boxes, Japheth had to use as many as large boxes as possible.

If Japheth used only large boxes,
number of large boxes used
= 330 ÷ 12
= 27 r 6 (x) There should be no remaining wafers left.

If 27 large boxes are used, there are 6 wafers left, Japheth had to use less large boxes so that the rest of the wafers were packed in small boxes.

If Japheth used 26 large boxes,
number of wafers to be packed in small boxes
= 330 - (26 x 12)
= 330 - 312
= 18

Number of small boxes needed to pack 18 wafers
= 18 ÷ 10
= 1 r 8 (x)

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

If Japheth used 25 large boxes,
number of wafers to be packed in small boxes
= 330 - (25 x 12)
= 330 - 300
= 30

Number of small boxes to pack 30 wafers
= 30 ÷ 10
= 3 r 0 (✓) There is no remaining wafers left.

Least number of boxes that Japheth used
= 25 + 3
= 28

Answer(s): 28