Divide $430 into 3 parts such that A gets 5/4 of B and the ratio between B and C is 3 : 4.

Let the three parts be $ A $, $ B $, and $ C $.

### Step 1: Set Up Relationships Between Parts
1. Given that $ A $ gets $\frac{5}{4}$ of $ B $, we can write:
   \[
   A = \frac{5}{4}B
   \]

2. The ratio between $ B $ and $ C $ is given as $ 3:4 $. So, we can express $ C $ in terms of $ B $:
   \[
   \frac{B}{C} = \frac{3}{4} \implies C = \frac{4}{3}B
   \]

### Step 2: Express Total Sum
The total sum of the parts is given as $ 430 $:
\[
A + B + C = 430
\]

Substituting the expressions for $ A $ and $ C $ in terms of $ B $:
\[
\frac{5}{4}B + B + \frac{4}{3}B = 430
\]

### Step 3: Simplify the Equation
Combine the terms by finding a common denominator. The common denominator of 4 and 3 is 12.

1. Convert each term:
   \[
   \frac{5}{4}B = \frac{15}{12}B, \quad B = \frac{12}{12}B, \quad \frac{4}{3}B = \frac{16}{12}B
   \]

2. Adding them:
   \[
   \frac{15}{12}B + \frac{12}{12}B + \frac{16}{12}B = \frac{43}{12}B
   \]

Thus, the equation becomes:
\[
\frac{43}{12}B = 430
\]

### Step 4: Solve for $ B $
Multiply both sides by 

Learn how to divide $430 into three parts, where A is 5/4 of B, and the ratio between B and C is 3:4. This step-by-step solution covers important algebraic concepts, including ratios, proportions, and solving linear equations. Suitable for students in Grades 9-12.

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