PSLE
Tim packed 366 tarts into large and small boxes. He filled each large box with 10 tarts and each small box with 6 tarts. All the boxes were full and no tarts were left over. What was the least number of boxes used by Tim?
To have the least number of boxes, Tim had to use as many as large boxes as possible.

If Tim used only large boxes,
number of large boxes used
= 366 ÷ 10
= 36 r 6 (x) There should be no remaining tarts left.

If 36 large boxes are used, there are 6 tarts left, Tim had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Tim used 35 large boxes,
number of tarts to be packed in small boxes
= 366 - (35 x 10)
= 366 - 350
= 16

Number of small boxes needed to pack 16 tarts
= 16 ÷ 6
= 2 r 4 (x)

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

If Tim used 34 large boxes,
number of tarts to be packed in small boxes
= 366 - (34 x 10)
= 366 - 340
= 26

Number of small boxes to pack 26 tarts
= 26 ÷ 6
= 4 r 2 (x)

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

If Tim used 33 large boxes,
number of tarts to be packed in small boxes
= 366 - (33 x 10)
= 366 - 330
= 36

Number of small boxes to pack 36 tarts
= 36 ÷ 6
= 6 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Tim used
= 33 + 6
= 39

Answer(s): 39