PSLE
Valen packed 444 shortbreads into large and small boxes. He filled each large box with 16 shortbreads and each small box with 10 shortbreads. All the boxes were full and no shortbreads were left over. What was the least number of boxes used by Valen?
To have the least number of boxes, Valen had to use as many as large boxes as possible.

If Valen used only large boxes,
number of large boxes used
= 444 ÷ 16
= 27 r 12 (x) There should be no remaining shortbreads left.

If 27 large boxes are used, there are 12 shortbreads left, Valen had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Valen used 26 large boxes,
number of shortbreads to be packed in small boxes
= 444 - (26 x 16)
= 444 - 416
= 28

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

There should be no remaining shortbreads left. So, Valen had to use less large boxes.

If Valen used 25 large boxes,
number of shortbreads to be packed in small boxes
= 444 - (25 x 16)
= 444 - 400
= 44

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

There should be no remaining shortbreads left. So, Valen had to use less large boxes.

If Valen used 24 large boxes,
number of shortbreads to be packed in small boxes
= 444 - (24 x 16)
= 444 - 384
= 60

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

Least number of boxes that Valen used
= 24 + 6
= 30

Answer(s): 30