PSLE
Eric packed 392 shortbreads into large and small boxes. He filled each large box with 18 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 Eric?
To have the least number of boxes, Eric had to use as many as large boxes as possible.

If Eric used only large boxes,
number of large boxes used
= 392 ÷ 18
= 21 r 14 (x) There should be no remaining shortbreads left.

If 21 large boxes are used, there are 14 shortbreads left, Eric had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Eric used 20 large boxes,
number of shortbreads to be packed in small boxes
= 392 - (20 x 18)
= 392 - 360
= 32

Number of small boxes needed to pack 32 shortbreads
= 32 ÷ 10
= 3 r 2 (x)

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

If Eric used 19 large boxes,
number of shortbreads to be packed in small boxes
= 392 - (19 x 18)
= 392 - 342
= 50

Number of small boxes to pack 50 shortbreads
= 50 ÷ 10
= 5 r 0 (✓) There is no remaining shortbreads left.

Least number of boxes that Eric used
= 19 + 5
= 24

Answer(s): 24