PSLE
Albert packed 472 cookies into large and small boxes. He filled each large box with 12 cookies and each small box with 10 cookies. All the boxes were full and no cookies were left over. What was the least number of boxes used by Albert?
To have the least number of boxes, Albert had to use as many as large boxes as possible.

If Albert used only large boxes,
number of large boxes used
= 472 ÷ 12
= 39 r 4 (x) There should be no remaining cookies left.

If 39 large boxes are used, there are 4 cookies left, Albert had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Albert used 38 large boxes,
number of cookies to be packed in small boxes
= 472 - (38 x 12)
= 472 - 456
= 16

Number of small boxes needed to pack 16 cookies
= 16 ÷ 10
= 1 r 6 (x)

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

If Albert used 37 large boxes,
number of cookies to be packed in small boxes
= 472 - (37 x 12)
= 472 - 444
= 28

Number of small boxes to pack 28 cookies
= 28 ÷ 10
= 2 r 8 (x)

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

If Albert used 36 large boxes,
number of cookies to be packed in small boxes
= 472 - (36 x 12)
= 472 - 432
= 40

Number of small boxes to pack 40 cookies
= 40 ÷ 10
= 4 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Albert used
= 36 + 4
= 40

Answer(s): 40