PSLE
Carl packed 364 cookies into large and small boxes. He filled each large box with 10 cookies and each small box with 8 cookies. All the boxes were full and no cookies were left over. What was the least number of boxes used by Carl?
To have the least number of boxes, Carl had to use as many as large boxes as possible.

If Carl used only large boxes,
number of large boxes used
= 364 ÷ 10
= 36 r 4 (x) There should be no remaining cookies left.

If 36 large boxes are used, there are 4 cookies left, Carl had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Carl used 35 large boxes,
number of cookies to be packed in small boxes
= 364 - (35 x 10)
= 364 - 350
= 14

Number of small boxes needed to pack 14 cookies
= 14 ÷ 8
= 1 r 6 (x)

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

If Carl used 34 large boxes,
number of cookies to be packed in small boxes
= 364 - (34 x 10)
= 364 - 340
= 24

Number of small boxes to pack 24 cookies
= 24 ÷ 8
= 3 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Carl used
= 34 + 3
= 37

Answer(s): 37