PSLE
Nick packed 230 shortbreads into large and small boxes. He filled each large box with 18 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 Nick?
To have the least number of boxes, Nick had to use as many as large boxes as possible.

If Nick used only large boxes,
number of large boxes used
= 230 ÷ 18
= 12 r 14 (x) There should be no remaining shortbreads left.

If 12 large boxes are used, there are 14 shortbreads left, Nick had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Nick used 11 large boxes,
number of shortbreads to be packed in small boxes
= 230 - (11 x 18)
= 230 - 198
= 32

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

Least number of boxes that Nick used
= 11 + 4
= 15

Answer(s): 15