PSLE
Ahmad packed 270 tarts into large and small boxes. He filled each large box with 12 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 Ahmad?
To have the least number of boxes, Ahmad had to use as many as large boxes as possible.

If Ahmad used only large boxes,
number of large boxes used
= 270 ÷ 12
= 22 r 6 (x) There should be no remaining tarts left.

If 22 large boxes are used, there are 6 tarts left, Ahmad had to use less large boxes so that the rest of the tarts were packed in small boxes.

If Ahmad used 21 large boxes,
number of tarts to be packed in small boxes
= 270 - (21 x 12)
= 270 - 252
= 18

Number of small boxes needed to pack 18 tarts
= 18 ÷ 10
= 1 r 8 (x)

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

If Ahmad used 20 large boxes,
number of tarts to be packed in small boxes
= 270 - (20 x 12)
= 270 - 240
= 30

Number of small boxes to pack 30 tarts
= 30 ÷ 10
= 3 r 0 (✓) There is no remaining tarts left.

Least number of boxes that Ahmad used
= 20 + 3
= 23

Answer(s): 23