PSLE
Flynn packed 482 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 Flynn?
To have the least number of boxes, Flynn had to use as many as large boxes as possible.

If Flynn used only large boxes,
number of large boxes used
= 482 ÷ 16
= 30 r 2 (x) There should be no remaining macarons left.

If 30 large boxes are used, there are 2 macarons left, Flynn had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Flynn used 29 large boxes,
number of macarons to be packed in small boxes
= 482 - (29 x 16)
= 482 - 464
= 18

Number of small boxes needed to pack 18 macarons
= 18 ÷ 10
= 1 r 8 (x)

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

If Flynn used 28 large boxes,
number of macarons to be packed in small boxes
= 482 - (28 x 16)
= 482 - 448
= 34

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

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

If Flynn used 27 large boxes,
number of macarons to be packed in small boxes
= 482 - (27 x 16)
= 482 - 432
= 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 Flynn used
= 27 + 5
= 32

Answer(s): 32