PSLE
Zeph packed 376 shortbreads into large and small boxes. He filled each large box with 18 shortbreads and each small box with 4 shortbreads. All the boxes were full and no shortbreads were left over. What was the least number of boxes used by Zeph?
To have the least number of boxes, Zeph had to use as many as large boxes as possible.

If Zeph used only large boxes,
number of large boxes used
= 376 ÷ 18
= 20 r 16 (x) There should be no remaining shortbreads left.

If 20 large boxes are used, there are 16 shortbreads left, Zeph had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Zeph used 19 large boxes,
number of shortbreads to be packed in small boxes
= 376 - (19 x 18)
= 376 - 342
= 34

Number of small boxes needed to pack 34 shortbreads
= 34 ÷ 4
= 8 r 2 (x)

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

If Zeph used 18 large boxes,
number of shortbreads to be packed in small boxes
= 376 - (18 x 18)
= 376 - 324
= 52

Number of small boxes to pack 52 shortbreads
= 52 ÷ 4
= 13 r 0 (✓) There is no remaining shortbreads left.

Least number of boxes that Zeph used
= 18 + 13
= 31

Answer(s): 31