Given that S=7a+b+7c and also S=6a+8b+6c, where 51< S < 149 and S is an integer, find the sum a+b+c.

Guest Nov 12, 2017

#1**+2 **

I have assumed that a,b,c are integers.....don't know if this is correct....!!!!

S=7a+b+7c

S=6a+8b+6c

Subtract the second equation from the first and rearrange

a + c = 7b

So using the first equation.........

S = 7 (a + c) + b ⇒ S = 49b + b = 50b

But since 51 < S < 149 and S is an integer.... then 51 < 50b < 149 ⇒ b = 2

So S = 100

So manipulating the first equation, we have

100 = 7a + 2 + 7c

98 = 7 (a + c) → a + c = 14

So.....the sum of a + b + c = (a + c) + b = 14 + 2 = 16

CPhill
Nov 12, 2017