we substitute the given expressions for a, b, and c into the equation and simplify it, to prove that a+b:b+c = 17:20.
To prove that a+b:b+c = 17:20, we need to substitute the given expressions for a, b, and c into the equation and simplify it. Let's start by finding the values of a, b, and c using the given equations:
From the first equation, 2a: 5c = 6:25, we can write:
2a/6 = 5c/25
2a/6 = c/5
10a = 6c
a = 6c/10
a = 3c/5
From the second equation, 4b: 7c = 20:21, we have:
4b/20 = 7c/21
b/5 = c/3
3b = 5c
b = 5c/3
Now, substitute these values into the equation a+b:b+c:
(3c/5 + 5c/3) : (c + 5c/3)
((9c + 25c)/15) : (3c + 15c/3)
(34c/15) : (3c + 5c)
(34c/15) : (8c)
34c : 120c
34 : 120
Therefore, a+b : b+c = 17:20.