orrect answerIf (a+b) : (b+c) : (c+a) = 5 : 7 : 6 and 2a -3b + 4c = 66 then value of c will be ?Options122418

The problem is a combination of ratio and algebraic equations. Here are the steps to solve it:

Step 1: Given that (a+b) : (b+c) : (c+a) = 5 : 7 : 6. This means that a+b, b+c, and c+a are in the ratio 5:7:6 respectively. Let's assume that a+b = 5x, b+c = 7x, and c+a = 6x for some real number x.

Step 2: Adding these three equations, we get 2a + 2b + 2c = 18x, which simplifies to a + b + c = 9x.

Step 3: We also know that 2a - 3b + 4c = 66.

Step 4: We need to find the value of c. To do this, we can express a and b in terms of c and x from the equations in step 1 and substitute them into the equation in step 3.

From a+b = 5x, we get a = 5x - b. From b+c = 7x, we get b = 7x - c.

Step 5: Substituting these values into the equation 2a - 3b + 4c = 66, we get:

2(5x - (7x - c)) - 3(7x - c) + 4c = 66 10x - 14x + 2c - 21x + 3c + 4c = 66 -25x + 9c = 66

Step 6: We also know that a + b + c = 9x. Substituting the values of a and b from step 4, we get:

(5x - (7x - c)) + (7x - c) + c = 9x 5x - 7x + c + 7x - c + c = 9x 5x = 9x - c

Step 7: Substituting 5x = 9x - c into the equation -25x + 9c = 66, we get:

-25(9x - c) + 9c = 66 -225x + 25c + 9c = 66 -225x + 34c = 66

Step 8: Solving for c, we get:

c = (66 + 225x) / 34 c = (66 + 225*5) / 34 c = 18

So, the value of c is 18.