# What is the value of c if 2a + b = c, a + b + c = 2d and a + b + c + d = 18, where a, b, c and d are positive integers?

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### 1 Answer

The value of c has to be determined given that 2a + b = c, a + b + c = 2d and a + b + c + d = 18

Substitute a + b + c = 2d in a + b + c + d = 18

=> 2d + d = 18

=> d = 6

a + b + c = 12 and 2a + b = c

=> c = 2*(12 - b - c) + b

=> c = 24 - 2b - 2c + b

=> 3c = 24 - b

=> c = 8 - b/3

As a, b, c and d are positive integers, of the values 3, 6, 9, 12, 15, 18 and 21 that b can take on with c being a positive number, b can take on only the values 3, 6 and 9 as a + b + c = 12. The corresponding value of c is 7, 6 and 5.

**The value of c is 5, 6 or 7**