PSLE
Eric packed 302 macarons into large and small boxes. He filled each large box with 14 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 Eric?
To have the least number of boxes, Eric had to use as many as large boxes as possible.

If Eric used only large boxes,
number of large boxes used
= 302 ÷ 14
= 21 r 8 (x) There should be no remaining macarons left.

If 21 large boxes are used, there are 8 macarons left, Eric had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Eric used 20 large boxes,
number of macarons to be packed in small boxes
= 302 - (20 x 14)
= 302 - 280
= 22

Number of small boxes needed to pack 22 macarons
= 22 ÷ 10
= 2 r 2 (x)

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

If Eric used 19 large boxes,
number of macarons to be packed in small boxes
= 302 - (19 x 14)
= 302 - 266
= 36

Number of small boxes to pack 36 macarons
= 36 ÷ 10
= 3 r 6 (x)

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

If Eric used 18 large boxes,
number of macarons to be packed in small boxes
= 302 - (18 x 14)
= 302 - 252
= 50

Number of small boxes to pack 50 macarons
= 50 ÷ 10
= 5 r 0 (✓) There is no remaining macarons left.

Least number of boxes that Eric used
= 18 + 5
= 23

Answer(s): 23