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 124 boxes of sunglasses. If there are more large boxes than smaller boxes, how many cartons did he ship?

Answer 1

A merchant selling sunglasses can place 8 large boxes or 10 small boxes into a carton for shipping.

If a total of 124 boxes are shipped, then the large boxes in the cartons must be a multiple of 8 which means either 16,56,64, 72,104.

We will choose that multiple of 8, which when subtracted from 124, gives the number that is divisible by 10.

As the larger boxes are more in quantity, we will choose 64 and 104.

`124-64=60`

`64/8=8` cartons

`60/10=6` cartons

Total cartons are =
`8+6=14`

Also,
`124-104=20`

`104/8=13` cartons

`20/10=2` cartons

So, total cartons shipped =
`13+2=15`

So, both can be answers. As any options are not given, you can solve it whatever way you like.

Answer 2

64 large boxes and 60 small boxes.

Explanation:

Here we must use the concept of multiples. A multiple of a number result of the multiplication of that number by an integer. For instance, 2, 4, 6, 8 are multiples of 2. The following chart shows our statement:

So we need to choose the number of small and large boxes such that the sum is 124 boxes of sunglasses and the number of large boxes is greater than the number of small boxes. From the table, the correct solution is:

64 large boxes and 60 small boxes because 64 + 60 = 124 and 64 > 60