PSLE
Eric packed 236 cookies into large and small boxes. He filled each large box with 10 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 Eric?
To have the least number of boxes, Eric had to use as many as large boxes as possible.

If Eric used only large boxes,
number of large boxes used
= 236 ÷ 10
= 23 r 6 (x) There should be no remaining cookies left.

If 23 large boxes are used, there are 6 cookies left, Eric had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Eric used 22 large boxes,
number of cookies to be packed in small boxes
= 236 - (22 x 10)
= 236 - 220
= 16

Number of small boxes needed to pack 16 cookies
= 16 ÷ 6
= 2 r 4 (x)

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

If Eric used 21 large boxes,
number of cookies to be packed in small boxes
= 236 - (21 x 10)
= 236 - 210
= 26

Number of small boxes to pack 26 cookies
= 26 ÷ 6
= 4 r 2 (x)

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

If Eric used 20 large boxes,
number of cookies to be packed in small boxes
= 236 - (20 x 10)
= 236 - 200
= 36

Number of small boxes to pack 36 cookies
= 36 ÷ 6
= 6 r 0 (✓) There is no remaining cookies left.

Least number of boxes that Eric used
= 20 + 6
= 26

Answer(s): 26