PSLE
Andy packed 282 cookies into large and small boxes. He filled each large box with 14 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 Andy?
To have the least number of boxes, Andy had to use as many as large boxes as possible.

If Andy used only large boxes,
number of large boxes used
= 282 ÷ 14
= 20 r 2 (x) There should be no remaining cookies left.

If 20 large boxes are used, there are 2 cookies left, Andy had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Andy used 19 large boxes,
number of cookies to be packed in small boxes
= 282 - (19 x 14)
= 282 - 266
= 16

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

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

If Andy used 18 large boxes,
number of cookies to be packed in small boxes
= 282 - (18 x 14)
= 282 - 252
= 30

Number of small boxes to pack 30 cookies
= 30 ÷ 10
= 3 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Andy used
= 18 + 3
= 21

Answer(s): 21