Question

Find the values of A and B in these equivalent ratios.
8:6 = 4:A = B:27
A= B=

Answer 1

To find the values of A and B in the equivalent ratios 8:6 = 4:A = B:27, one must set up proportions and solve them. By cross-multiplying, A is determined to be 3 and B is determined to be 36.

Step-by-step explanation:

The student has asked to find the values of A and B in these equivalent ratios: 8:6 = 4:A = B:27. To solve for A and B, we can set up proportions because the ratios are equivalent. For the first ratio, we can write 8/6 = 4/A, and by cross-multiplying, we find that A equals 3. For the second ratio, B/27 = 4/A, substituting A = 3 into the equation, we find that B equals 8.

Let's solve the equations step by step:

1. For A, the proportion is 8/6 = 4/A. Cross-multiplying gives 8A = 24, and solving for A we get A = 3.
2. For B, using A = 3, the proportion is B/27 = 4/3. Cross-multiplying gives 3B = 108, and solving for B we get B = 36.