Solving the Ratio Problem: 30 of A 0.25 of B 1/5th of C

In this article, we will explore how to solve a complex ratio problem involving the relationships between three variables, A, B, and C. The problem states that '30 of A 0.25 of B 1/5th of C'. We will break down the steps needed to find the ratio between A, B, and C, making use of algebraic manipulation to simplify and solve the problem. By the end of this article, you will be able to understand and solve similar ratio problems.

Introduction to the Problem

The problem given is to find the ratio of A : B : C, given the equation 30 of A 0.25 of B 1/5th of C. We'll start by defining a common variable k for all the expressions mentioned in the problem.

Defining the Variables

Let:

30 of A 0.25 of B 1/5th of C k

This means that, mathematically, we can set:

30A k
0.25B k
C/5 k

Solving for A, B, and C

Using the equation for each variable:

From 30A k: A k/30 (10k)/30 (10k)/30 10k/30 10k/3

From 0.25B k: B k/0.25 4k

From C/5 k: C 5k

Now, we have:

A 10k/3, B 4k, C 5k

Finding the Ratio A : B : C

To find the ratio of A : B : C, we can express it as:

A : B : C (10k/3) : 4k : 5k

To simplify, we can eliminate k by dividing each term by k:

(10/3) : 4 : 5

Next, we need to convert all parts to a common denominator. The least common multiple of 3, 1, and 1 is 3. So, multiplying each part by 3, we get:

(10/3) × 3 : 4 × 3 : 5 × 3 10 : 12 : 15

Finally, to further simplify the ratio, we can divide each term by the greatest common divisor (GCD), which is 5:

10/5 : 12/5 : 15/5 2 : 2.4 : 3

Expressing it in whole numbers, we multiply through by 5:

10 : 12 : 15

Therefore, the final simplified ratio is:

boxed{10 : 12 : 15}

Conclusion

Solving the ratio problem '30 of A 0.25 of B 1/5th of C' involves setting up equations and simplifying them step-by-step. We used algebraic manipulation to eliminate the common variable and find the ratio between the three variables. Understanding these steps and practicing similar problems will help improve your skills in solving complex ratio problems.

References:

Solving for A, B, and C: Using algebraic equations and simplifying them. Common Denominator: Finding the least common multiple of the denominators. Greatest Common Divisor (GCD): Dividing terms by the GCD to simplify the ratio.