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

9514 1404 393

  11 cartons

Step-by-step explanation:

By shipping all 96 boxes as large boxes, the merchant will have shipped

  (96 boxes)/(8 boxes/large carton) = 12 large cartons*

He can ship as many boxes in 4 cartons of small boxes as in 5 cartons of large boxes. So trading 5 cartons of large boxes for 4 cartons of small boxes, he can reduce the number of cartons shipped by 1.

The merchant shipped 11 cartons:

  7 cartons of large boxes (56 large boxes)

  4 cartons of small boxes (40 small boxes)

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Any further such trade would reduce the number of large boxes to fewer than small boxes, violating the problem constraint.

* In this expression, we use the term "large carton" to mean "carton of large boxes".

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13