What is c if: a+b+c = 77, a-c = b+c, and c = b/2
a = b + 2 c
b = 2 c
so a = 2 c + 2c = 4 c
a + b + c = 77
4 c + 2 c + c = 77
7 c = 77
c = 11
Thanks!
You are welcome.
To find the value of c, we can substitute the given equations into each other.
Given:
a + b + c = 77 --(1)
a - c = b + c --(2)
c = b / 2 --(3)
Let's substitute equation (3) into equations (1) and (2):
From equation (1):
a + b + c = 77
a + b + (b/2) = 77 (substituting c = b/2)
(2a + 2b + b)/2 = 77
(2a + 3b)/2 = 77
2a + 3b = 77 * 2
2a + 3b = 154 --(4)
From equation (2):
a - c = b + c
a - (b/2) = b + (b/2) (substituting c = b/2)
a - b/2 = (3b/2)
2a/2 - b/2 = (3b/2)
2a - b = 3b
2a = 4b
a = 2b --(5)
Now, we have two equations in terms of a and b:
2a + 3b = 154 --(4)
a = 2b --(5)
Let's solve these equations to find the values of a and b.