If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is:

Question

Solve for $x$: \[ \frac{4}{x} - \frac{5}{2x + 3} = 3. \]

Answer 1

To determine the ratio A + B : B + C : A + C, given A : B = 5 : 6 and B : C = 6 : 7, we first establish a common representation for A, B, and C. Let B = 6x. Consequently:

From A : B = 5 : 6, we derive A = 5x.
From B : C = 6 : 7, we derive C = 7x.

Next, we compute each component of the target ratio:

A + B = 5x + 6x = 11x
B + C = 6x + 7x = 13x
A + C = 5x + 7x = 12x

Thus, the ratio A + B : B + C : A + C is expressed as:

11x : 13x : 12x

This simplifies to:

11 : 13 : 12

The definitive answer is 11 : 13 : 12.

If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is:

The Correct Option is B

Solution and Explanation

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