PSLE
Harry packed 444 cookies into large and small boxes. He filled each large box with 16 cookies and each small box with 6 cookies. All the boxes were full and no cookies were left over. What was the least number of boxes used by Harry?
To have the least number of boxes, Harry had to use as many as large boxes as possible.

If Harry used only large boxes,
number of large boxes used
= 444 ÷ 16
= 27 r 12 (x) There should be no remaining cookies left.

If 27 large boxes are used, there are 12 cookies left, Harry had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Harry used 26 large boxes,
number of cookies to be packed in small boxes
= 444 - (26 x 16)
= 444 - 416
= 28

Number of small boxes needed to pack 28 cookies
= 28 ÷ 6
= 4 r 4 (x)

There should be no remaining cookies left. So, Harry had to use less large boxes.

If Harry used 25 large boxes,
number of cookies to be packed in small boxes
= 444 - (25 x 16)
= 444 - 400
= 44

Number of small boxes to pack 44 cookies
= 44 ÷ 6
= 7 r 2 (x)

There should be no remaining cookies left. So, Harry had to use less large boxes.

If Harry used 24 large boxes,
number of cookies to be packed in small boxes
= 444 - (24 x 16)
= 444 - 384
= 60

Number of small boxes to pack 60 cookies
= 60 ÷ 6
= 10 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Harry used
= 24 + 10
= 34

Answer(s): 34