PSLE
Ivan packed 466 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 Ivan?
To have the least number of boxes, Ivan had to use as many as large boxes as possible.

If Ivan used only large boxes,
number of large boxes used
= 466 ÷ 10
= 46 r 6 (x) There should be no remaining cookies left.

If 46 large boxes are used, there are 6 cookies left, Ivan had to use less large boxes so that the rest of the cookies were packed in small boxes.

If Ivan used 45 large boxes,
number of cookies to be packed in small boxes
= 466 - (45 x 10)
= 466 - 450
= 16

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

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

If Ivan used 44 large boxes,
number of cookies to be packed in small boxes
= 466 - (44 x 10)
= 466 - 440
= 26

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

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

If Ivan used 43 large boxes,
number of cookies to be packed in small boxes
= 466 - (43 x 10)
= 466 - 430
= 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 Ivan used
= 43 + 6
= 49

Answer(s): 49