PSLE
Ken packed 410 macarons into large and small boxes. He filled each large box with 16 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 Ken?
To have the least number of boxes, Ken had to use as many as large boxes as possible.

If Ken used only large boxes,
number of large boxes used
= 410 ÷ 16
= 25 r 10 (x) There should be no remaining macarons left.

If 25 large boxes are used, there are 10 macarons left, Ken had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Ken used 24 large boxes,
number of macarons to be packed in small boxes
= 410 - (24 x 16)
= 410 - 384
= 26

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

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

If Ken used 23 large boxes,
number of macarons to be packed in small boxes
= 410 - (23 x 16)
= 410 - 368
= 42

Number of small boxes to pack 42 macarons
= 42 ÷ 6
= 7 r 0 (✓) There is no remaining macarons left.

Least number of boxes that Ken used
= 23 + 7
= 30

Answer(s): 30