PSLE
Bryan packed 220 tarts into large and small boxes. He filled each large box with 16 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 Bryan?
To have the least number of boxes, Bryan had to use as many as large boxes as possible.

If Bryan used only large boxes,
number of large boxes used
= 220 ÷ 16
= 13 r 12 (x) There should be no remaining tarts left.

If 13 large boxes are used, there are 12 tarts left, Bryan had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Bryan used 12 large boxes,
number of tarts to be packed in small boxes
= 220 - (12 x 16)
= 220 - 192
= 28

Number of small boxes needed to pack 28 tarts
= 28 ÷ 6
= 4 r 4 (x)

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

If Bryan used 11 large boxes,
number of tarts to be packed in small boxes
= 220 - (11 x 16)
= 220 - 176
= 44

Number of small boxes to pack 44 tarts
= 44 ÷ 6
= 7 r 2 (x)

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

If Bryan used 10 large boxes,
number of tarts to be packed in small boxes
= 220 - (10 x 16)
= 220 - 160
= 60

Number of small boxes to pack 60 tarts
= 60 ÷ 6
= 10 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Bryan used
= 10 + 10
= 20

Answer(s): 20