PSLE
Tommy packed 264 shortbreads into large and small boxes. He filled each large box with 10 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 Tommy?
To have the least number of boxes, Tommy had to use as many as large boxes as possible.

If Tommy used only large boxes,
number of large boxes used
= 264 ÷ 10
= 26 r 4 (x) There should be no remaining shortbreads left.

If 26 large boxes are used, there are 4 shortbreads left, Tommy had to use less large boxes so that the rest of the shortbreads were packed in small boxes.

If Tommy used 25 large boxes,
number of shortbreads to be packed in small boxes
= 264 - (25 x 10)
= 264 - 250
= 14

Number of small boxes needed to pack 14 shortbreads
= 14 ÷ 8
= 1 r 6 (x)

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

If Tommy used 24 large boxes,
number of shortbreads to be packed in small boxes
= 264 - (24 x 10)
= 264 - 240
= 24

Number of small boxes to pack 24 shortbreads
= 24 ÷ 8
= 3 r 0 (✓) There is no remaining shortbreads left.

Least number of boxes that Tommy used
= 24 + 3
= 27

Answer(s): 27