PSLE
Tom packed 342 tarts into large and small boxes. He filled each large box with 14 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 Tom?
To have the least number of boxes, Tom had to use as many as large boxes as possible.

If Tom used only large boxes,
number of large boxes used
= 342 ÷ 14
= 24 r 6 (x) There should be no remaining tarts left.

If 24 large boxes are used, there are 6 tarts left, Tom had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Tom used 23 large boxes,
number of tarts to be packed in small boxes
= 342 - (23 x 14)
= 342 - 322
= 20

Number of small boxes needed to pack 20 tarts
= 20 ÷ 8
= 2 r 4 (x)

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

If Tom used 22 large boxes,
number of tarts to be packed in small boxes
= 342 - (22 x 14)
= 342 - 308
= 34

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

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

If Tom used 21 large boxes,
number of tarts to be packed in small boxes
= 342 - (21 x 14)
= 342 - 294
= 48

Number of small boxes to pack 48 tarts
= 48 ÷ 8
= 6 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Tom used
= 21 + 6
= 27

Answer(s): 27