If 5A = 13B = 7C; find the value of A : B : C.

Let's solve this step by step:

Step 1: We are given that 5A = 13B = 7C. This means that 5A, 13B, and 7C are all equal to the same value. Let's call this value X. So we have:

5A = X 13B = X 7C = X

Step 2: Now, we can express A, B, and C in terms of X:

A = X/5 B = X/13 C = X/7

Step 3: We want to find the ratio A : B : C. Substituting the expressions we found in step 2, we get:

A : B : C = X/5 : X/13 : X/7

Step 4: The X's cancel out in the ratio, so we are left with:

A : B : C = 1/5 : 1/13 : 1/7

Step 5: To make the ratio easier to understand, we can find the least common multiple (LCM) of 5, 13, and 7, which is 455. Multiply each part of the ratio by 455:

A : B : C = 455/5 : 455/13 : 455/7

Step 6: Simplify each part of the ratio:

A : B : C = 91 : 35 : 65

So, the ratio of A : B : C is 91 : 35 : 65.