PSLE
Vincent packed 412 macarons into large and small boxes. He filled each large box with 18 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 Vincent?
To have the least number of boxes, Vincent had to use as many as large boxes as possible.

If Vincent used only large boxes,
number of large boxes used
= 412 ÷ 18
= 22 r 16 (x) There should be no remaining macarons left.

If 22 large boxes are used, there are 16 macarons left, Vincent had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Vincent used 21 large boxes,
number of macarons to be packed in small boxes
= 412 - (21 x 18)
= 412 - 378
= 34

Number of small boxes needed to pack 34 macarons
= 34 ÷ 10
= 3 r 4 (x)

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

If Vincent used 20 large boxes,
number of macarons to be packed in small boxes
= 412 - (20 x 18)
= 412 - 360
= 52

Number of small boxes to pack 52 macarons
= 52 ÷ 10
= 5 r 2 (x)

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

If Vincent used 19 large boxes,
number of macarons to be packed in small boxes
= 412 - (19 x 18)
= 412 - 342
= 70

Number of small boxes to pack 70 macarons
= 70 ÷ 10
= 7 r 0 (✓) There is no remaining macarons left.

Least number of boxes that Vincent used
= 19 + 7
= 26

Answer(s): 26