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2a: 5c = 6:25
4b:7c=20:21
Show that a+b:b+c=17:20

1 Answer

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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.

User Jeremiah Rose
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