PSLE
Justin packed 232 macarons into large and small boxes. He filled each large box with 10 macarons and each small box with 8 macarons. All the boxes were full and no macarons were left over. What was the least number of boxes used by Justin?
To have the least number of boxes, Justin had to use as many as large boxes as possible.

If Justin used only large boxes,
number of large boxes used
= 232 ÷ 10
= 23 r 2 (x) There should be no remaining macarons left.

If 23 large boxes are used, there are 2 macarons left, Justin had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Justin used 22 large boxes,
number of macarons to be packed in small boxes
= 232 - (22 x 10)
= 232 - 220
= 12

Number of small boxes needed to pack 12 macarons
= 12 ÷ 8
= 1 r 4 (x)

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

If Justin used 21 large boxes,
number of macarons to be packed in small boxes
= 232 - (21 x 10)
= 232 - 210
= 22

Number of small boxes to pack 22 macarons
= 22 ÷ 8
= 2 r 6 (x)

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

If Justin used 20 large boxes,
number of macarons to be packed in small boxes
= 232 - (20 x 10)
= 232 - 200
= 32

Number of small boxes to pack 32 macarons
= 32 ÷ 8
= 4 r 0 (✓) There is no remaining macarons left.

Least number of boxes that Justin used
= 20 + 4
= 24

Answer(s): 24