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Class 12 Tuition > Learn Mathematics > If a +b + c =100 And 1000 a + 300b + 50c = 10000. How Many Such Triplets...
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If a +b + c =100 And 1000 a + 300b + 50c = 10000. How Many Such Triplets a, b, c Are Possible?

Sujoy Das
07/02/2018 0 0

Question:

If a +b + c =100 and 1000a + 300b + 50c = 10000.How many such triplets a,b,c are possible?

 

Answer:

Method 1:

First equation : 50 a + 50 b + 50 c = 5000

And 1000 a + 300b + 50 c = 10,000

Subtracting: 19a + 5b = 100

Solution set for this is infinte (5,1) (0,20), (-5, 39), (-10, 58)

c will assume values depending upon a and b.

Hence Infinite!

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