PSLE
Riordan packed 368 shortbreads into large and small boxes. He filled each large box with 12 shortbreads and each small box with 8 shortbreads. All the boxes were full and no shortbreads were left over. What was the least number of boxes used by Riordan?
To have the least number of boxes, Riordan had to use as many as large boxes as possible.

If Riordan used only large boxes,
number of large boxes used
= 368 ÷ 12
= 30 r 8 (x) There should be no remaining shortbreads left.

If 30 large boxes are used, there are 8 shortbreads left, Riordan had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Riordan used 29 large boxes,
number of shortbreads to be packed in small boxes
= 368 - (29 x 12)
= 368 - 348
= 20

Number of small boxes needed to pack 20 shortbreads
= 20 ÷ 8
= 2 r 4 (x)

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

If Riordan used 28 large boxes,
number of shortbreads to be packed in small boxes
= 368 - (28 x 12)
= 368 - 336
= 32

Number of small boxes to pack 32 shortbreads
= 32 ÷ 8
= 4 r 0 (✓) There is no remaining shortbreads left.

Least number of boxes that Riordan used
= 28 + 4
= 32

Answer(s): 32