Question

a:b:c=3:4:1 and b:c:d=5:3:2 finda:b,c:d​

Answer 1

a:b =2:3

b:c = 4:5

c:d = 6:7

A:D = ?

We’ll start with the first equation:

a:b = 2:3

Now a and b can be any numbers provided they maintain a 2:3 ratio. However, when it is re-written as a fraction and reduced it is still equal to 2/3. An example of this would be 30/45, in which both the numerator and denominator share a GCF of 15.

So, we can assume that since a:b = 2:3 a = 2 and b = 3

This means that:

a/b = 2/3 where a = 2 and b = 3

Now, for b:c we have a different ratio. Remember, all four variables, by themselves, have the same value in each equation. Thus if b/c = 4/5, and b = 3, then c = 3.75. Both b and c are divisible by 0.75.

So a/b = 2/3

b/c = 3/3.75

So c = 3.75. This bring us to the next equation:

c:d = 6:7

In this example, we have 3.75 / d in a ratio of 6:7. Divide 3.75 by 6 and then multiply by 7 to find D:

3.75 * 6 = 0.625

0.625 * 7 = 4.375

You can double-check by dividing 3.75 by 4.375. It is approximately 0.857. Then divide 6 by 7 and you will come to the same result.

Thus, A:D = 2/4.375, or approximately 0.457

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