PSLE
Ivan packed 400 cupcakes into large and small boxes. He filled each large box with 14 cupcakes and each small box with 10 cupcakes. All the boxes were full and no cupcakes 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
= 400 ÷ 14
= 28 r 8 (x) There should be no remaining cupcakes left.

If 28 large boxes are used, there are 8 cupcakes left, Ivan had to use less large boxes so that the rest of the cupcakes were packed in small boxes.

If Ivan used 27 large boxes,
number of cupcakes to be packed in small boxes
= 400 - (27 x 14)
= 400 - 378
= 22

Number of small boxes needed to pack 22 cupcakes
= 22 ÷ 10
= 2 r 2 (x)

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

If Ivan used 26 large boxes,
number of cupcakes to be packed in small boxes
= 400 - (26 x 14)
= 400 - 364
= 36

Number of small boxes to pack 36 cupcakes
= 36 ÷ 10
= 3 r 6 (x)

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

If Ivan used 25 large boxes,
number of cupcakes to be packed in small boxes
= 400 - (25 x 14)
= 400 - 350
= 50

Number of small boxes to pack 50 cupcakes
= 50 ÷ 10
= 5 r 0 (✓) There is no remaining cupcakes left.

Least number of boxes that Ivan used
= 25 + 5
= 30

Answer(s): 30