PSLE
Brandon packed 316 tarts into large and small boxes. He filled each large box with 14 tarts and each small box with 10 tarts. All the boxes were full and no tarts were left over. What was the least number of boxes used by Brandon?
To have the least number of boxes, Brandon had to use as many as large boxes as possible.

If Brandon used only large boxes,
number of large boxes used
= 316 ÷ 14
= 22 r 8 (x) There should be no remaining tarts left.

If 22 large boxes are used, there are 8 tarts left, Brandon had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Brandon used 21 large boxes,
number of tarts to be packed in small boxes
= 316 - (21 x 14)
= 316 - 294
= 22

Number of small boxes needed to pack 22 tarts
= 22 ÷ 10
= 2 r 2 (x)

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

If Brandon used 20 large boxes,
number of tarts to be packed in small boxes
= 316 - (20 x 14)
= 316 - 280
= 36

Number of small boxes to pack 36 tarts
= 36 ÷ 10
= 3 r 6 (x)

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

If Brandon used 19 large boxes,
number of tarts to be packed in small boxes
= 316 - (19 x 14)
= 316 - 266
= 50

Number of small boxes to pack 50 tarts
= 50 ÷ 10
= 5 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Brandon used
= 19 + 5
= 24

Answer(s): 24