PSLE
Liam packed 434 tarts into large and small boxes. He filled each large box with 10 tarts and each small box with 8 tarts. All the boxes were full and no tarts were left over. What was the least number of boxes used by Liam?
To have the least number of boxes, Liam had to use as many as large boxes as possible.

If Liam used only large boxes,
number of large boxes used
= 434 ÷ 10
= 43 r 4 (x) There should be no remaining tarts left.

If 43 large boxes are used, there are 4 tarts left, Liam had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Liam used 42 large boxes,
number of tarts to be packed in small boxes
= 434 - (42 x 10)
= 434 - 420
= 14

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

There should be no remaining tarts left. So, Liam had to use less large boxes.

If Liam used 41 large boxes,
number of tarts to be packed in small boxes
= 434 - (41 x 10)
= 434 - 410
= 24

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

Least number of boxes that Liam used
= 41 + 3
= 44

Answer(s): 44