Question

A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment, he sent a total of 96 boxes of hamburger buns. If there are more large boxes than small boxes, how many cartons did he ship?

Answer 1

11 boxes total 4 small 7 large

Explanation:

1 small box *10 = 10 96-10 = 86 (NO MULTIPLE OF 8)

2 small boxes*10=20 96-29=76 ( no multiple of 8)

3 small boxes *10=30 96-30= 66(no multiple of 8)

4 small boxes*10 = 40 96-40 = 56 (YES multiple of 8) 56/8 = 7 (7 large boxes)

4 large boxes and 7 large boxes

Answer 2

11 cartons

Explanation:

Number of large boxes that can be contained in a carton = 8

Number of small boxes that can be contained in a carton = 10

Total number of boxes sent in one shipment = 96

This shipment contains both large and small boxes. Let there be x cartons of large boxes and y cartons of small boxes in one shipment. So, we can say,

Total number of large boxes in one shipment = Number of boxes in one carton * Total number of cartons = 8x

Similarly,

Total number of small boxes in one shipment = 10y

Since, total number of boxes in one shipment is 96, we can set up the equation as:

8x + 10y = 96

This equation can have following possible solutions:

• x =2, y = 8
• x = 7, y = 4
• x = 12, y = 0

We are given in the statement that are more large boxes than the small boxes, the valid solutions are:

• x = 7, y = 4
• x = 12, y = 0

Assuming that he sent both large and small boxes, the only valid solution will be:

• x = 7, y = 4

This means, the merchant sent 7 cartons of large boxes i.e. 56 large boxes and 4 cartons of small boxes i.e. 40 small boxes. So in total he sent 11 cartons.