PSLE
Ahmad packed 446 macarons into large and small boxes. He filled each large box with 10 macarons and each small box with 6 macarons. All the boxes were full and no macarons 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
= 446 ÷ 10
= 44 r 6 (x) There should be no remaining macarons left.

If 44 large boxes are used, there are 6 macarons left, Ahmad had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Ahmad used 43 large boxes,
number of macarons to be packed in small boxes
= 446 - (43 x 10)
= 446 - 430
= 16

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

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

If Ahmad used 42 large boxes,
number of macarons to be packed in small boxes
= 446 - (42 x 10)
= 446 - 420
= 26

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

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

If Ahmad used 41 large boxes,
number of macarons to be packed in small boxes
= 446 - (41 x 10)
= 446 - 410
= 36

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

Least number of boxes that Ahmad used
= 41 + 6
= 47

Answer(s): 47