PSLE
Ivan packed 476 wafers into large and small boxes. He filled each large box with 16 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 Ivan?
To have the least number of boxes, Ivan had to use as many as large boxes as possible.

If Ivan used only large boxes,
number of large boxes used
= 476 ÷ 16
= 29 r 12 (x) There should be no remaining wafers left.

If 29 large boxes are used, there are 12 wafers left, Ivan had to use less large boxes so that the rest of the wafers were packed in small boxes.

If Ivan used 28 large boxes,
number of wafers to be packed in small boxes
= 476 - (28 x 16)
= 476 - 448
= 28

Number of small boxes needed to pack 28 wafers
= 28 ÷ 10
= 2 r 8 (x)

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

If Ivan used 27 large boxes,
number of wafers to be packed in small boxes
= 476 - (27 x 16)
= 476 - 432
= 44

Number of small boxes to pack 44 wafers
= 44 ÷ 10
= 4 r 4 (x)

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

If Ivan used 26 large boxes,
number of wafers to be packed in small boxes
= 476 - (26 x 16)
= 476 - 416
= 60

Number of small boxes to pack 60 wafers
= 60 ÷ 10
= 6 r 0 (✓) There is no remaining wafers left.

Least number of boxes that Ivan used
= 26 + 6
= 32

Answer(s): 32