PSLE
Elijah packed 396 macarons into large and small boxes. He filled each large box with 16 macarons and each small box with 10 macarons. All the boxes were full and no macarons were left over. What was the least number of boxes used by Elijah?
To have the least number of boxes, Elijah had to use as many as large boxes as possible.

If Elijah used only large boxes,
number of large boxes used
= 396 ÷ 16
= 24 r 12 (x) There should be no remaining macarons left.

If 24 large boxes are used, there are 12 macarons left, Elijah had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Elijah used 23 large boxes,
number of macarons to be packed in small boxes
= 396 - (23 x 16)
= 396 - 368
= 28

Number of small boxes needed to pack 28 macarons
= 28 ÷ 10
= 2 r 8 (x)

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

If Elijah used 22 large boxes,
number of macarons to be packed in small boxes
= 396 - (22 x 16)
= 396 - 352
= 44

Number of small boxes to pack 44 macarons
= 44 ÷ 10
= 4 r 4 (x)

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

If Elijah used 21 large boxes,
number of macarons to be packed in small boxes
= 396 - (21 x 16)
= 396 - 336
= 60

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

Least number of boxes that Elijah used
= 21 + 6
= 27

Answer(s): 27