Lexie is a boat maker and makes scale-model versions of the exact same model boa

Question

Lexie is a boat maker and makes scale-model versions of the exact same model boat starting at 10" length and increasing by 10" each; the largest boat in her collection is 150" long. (i.e. her collection contains the same boat but at 10" long, 20" long, 30" long, ... 150" long). Lexie plans on painting some of her boats but she has only one can or paint - it will exactly cover the 130" boat (with no leftover paint). Instead of painting just the single of 130" boat, which two boats could the one can paint instead? (i.e both boats are completely covered and there is no leftover paint) Which three boats could the one paint instead? (all three boats are completely covered and there is no leftover paint)

Explanation / Answer

Solution -

a) Lexie's collection contains boats of following lengths -

10,20,30,40,50,60,70,80,90,100,110,120,130,140, 150.

We can choose any two boats which have sum of lengths 130''.

So there are following possibilities

10 and 120

20 and 110

30 and 100

40 and 90

50 and 80

60 and 70   

We can choose any one combination from these.

b)

We can choose any three boats which have sum of lengths 130''.

Some combinations are following-

10, 20, 100

20,30,80

30, 40, 60

50,60, 20

80,30,20

40,70,20

  

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