PSLE
Ryan packed 278 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 Ryan?
To have the least number of boxes, Ryan had to use as many as large boxes as possible.

If Ryan used only large boxes,
number of large boxes used
= 278 ÷ 16
= 17 r 6 (x) There should be no remaining macarons left.

If 17 large boxes are used, there are 6 macarons left, Ryan had to use less large boxes so that the rest of the macarons were packed in small boxes.

If Ryan used 16 large boxes,
number of macarons to be packed in small boxes
= 278 - (16 x 16)
= 278 - 256
= 22

Number of small boxes needed to pack 22 macarons
= 22 ÷ 6
= 3 r 4 (x)

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

If Ryan used 15 large boxes,
number of macarons to be packed in small boxes
= 278 - (15 x 16)
= 278 - 240
= 38

Number of small boxes to pack 38 macarons
= 38 ÷ 6
= 6 r 2 (x)

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

If Ryan used 14 large boxes,
number of macarons to be packed in small boxes
= 278 - (14 x 16)
= 278 - 224
= 54

Number of small boxes to pack 54 macarons
= 54 ÷ 6
= 9 r 0 (✓) There is no remaining macarons left.

Least number of boxes that Ryan used
= 14 + 9
= 23

Answer(s): 23