PSLE
Caden packed 274 wafers into large and small boxes. He filled each large box with 10 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 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
= 274 ÷ 10
= 27 r 4 (x) There should be no remaining wafers left.

If 27 large boxes are used, there are 4 wafers left, Caden had to use less large boxes so that the rest of the wafers were packed in small boxes.

If Caden used 26 large boxes,
number of wafers to be packed in small boxes
= 274 - (26 x 10)
= 274 - 260
= 14

Number of small boxes needed to pack 14 wafers
= 14 ÷ 4
= 3 r 2 (x)

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

If Caden used 25 large boxes,
number of wafers to be packed in small boxes
= 274 - (25 x 10)
= 274 - 250
= 24

Number of small boxes to pack 24 wafers
= 24 ÷ 4
= 6 r 0 (✓) There is no remaining wafers left.

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

Answer(s): 31