Question

A/b=c/d=k , 3a-4c/36-12d=k/3, b=? ​

Answer 1

$\frac{a}{b} = \frac{c}{d} = k \\ \frac{3a - 4c}{36 - 12d} = \frac{k}{3} \\ \frac{3a - 4c}{3(12 -4 d)} = \frac{k}{3} \\ \frac{3a - 4c}{12 - 4d} = k \\ \frac{3a - 4c}{12 - 4d} = \frac{c}{d} \\ 3ad - 4cd = 12c - 4cd \\ ad = 4c \\ ad = cb \\ = > cb = 4c \\ b = 4.$

Answer 2

To find the value of 'b,' we can use the information provided in the equations. Let's solve step by step:

1. Given: A/b = c/d = k

2. From the first equation, we can express 'A' and 'c' in terms of 'b' and 'd': A = b * k c = d * k

3. Next, we are given the second equation: (3a - 4c) / (36 - 12d) = k / 3

4. Substitute the expressions for 'A' and 'c' into the equation: (3 * b * k - 4 * d * k) / (36 - 12 * d) = k / 3

5. Simplify the equation: (3 * k * (b - 4d)) / (36 - 12d) = k / 3

6. Cross-multiply: 3 * k * (b - 4d) * 3 = k * (36 - 12d)

7. Cancel out 'k' from both sides: 3 * (b - 4d) * 3 = 36 - 12d

8. Simplify and solve for 'b': 9 * (b - 4d) = 36 - 12d

9. Expand: 9b - 36d = 36 - 12d

10. Move the terms with 'b' to one side: 9b = 36 - 12d + 36d

11. Simplify: 9b = 36 + 24d

12. Divide by 9 to isolate 'b': b = (36 + 24d) / 9

So, the value of 'b' is given by: b = (36 + 24d) / 9