Question

A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 566 boxes of sunglasses. If there are more large boxes than small boxes, how many cartons did he ship?

Answer 1

answer : 69 or 70

a/c to question,

capacity of each cartoon = 8 large boxes of sunglass or 10 small boxes of sunglass.

again, total number of sunglasses = 566

Let number of large sunglasses are x and small sunglasses are y.

so, x + y = 566....(1) , where x and y are positive integers .

and number of cartoons = x/8 + y/10 [ it should be integer value ]....(2)

also given, x > y ....(3)

divides the 566 in such a way that it will follow equations (1), (2) and (3)

we know, 8 ends with 6 only for two time, when it is multiply by 2 or its multiply by 7.

so, by this clue,

case 1 : if we assume x = 536 and y = 30

then, x/8 = 536/8 = 67

y/10 = 30/10 = 3

hence, total number of cartoons = 67 + 3 = 70

case 2 : if we assume x = 496 and y = 70

then, number of cartoons = x/8 + y/10

= 496/8 + 70/10

= 62 + 7

= 69

hence, total number of cartoons = 69