If a: b=5:9 and b:c=4:7 then what is a:b:c

To find the ratio \( a : b : c \), we need to combine the given ratios \( a : b = 5 : 9 \) and \( b : c = 4 : 7 \).

### Step 1: Express \( b \) in terms of both ratios.
- From \( a : b = 5 : 9 \), let \( a = 5k \) and \( b = 9k \).
- From \( b : c = 4 : 7 \), let \( b = 4m \) and \( c = 7m \).

### Step 2: Equate the values of \( b \).
- Since \( b = 9k \) and \( b = 4m \), equate these: \( 9k = 4m \).

### Step 3: Solve for \( k \) and \( m \).
- \( k = \frac{4m}{9} \).

### Step 4: Express \( a \), \( b \), and \( c \) in terms of \( m \).
- \( a = 5k = 5 \times \frac{4m}{9} = \frac{20m}{9} \).
- \( b = 9k = 9 \times \frac{4m}{9} = 4m \).
- \( c = 7m \).

### Step 5: Find the ratio \( a : b : c \).
- \( a : b : c = \frac{20m}{9} : 4m : 7m \).

To eliminate \( m \) and simplify:
- Multiply each term by 9 to clear the denominator for \( a \):  
  \( 20 : 36 : 63 \).

### Final Answer:
The ratio \( a : b : c = 20 : 36 : 63 \).

Would you like a detailed explanation of any steps, or do you have any questions? Here are some related questions you might find interesting:

1. If the ratio \( a : b \) changes, how would it affect \( a : b : c \)?
2. How do you solve for three variables when given multiple ratios?
3. Can you express \( a : c \) directly from the given ratios?
4. How would the result change if the second ratio was \( b : c = 3 : 7 \) instead?
5. What is the importance of clearing denominators in ratios?

**Tip:** When dealing with ratios, always ensure to express the common terms in a consistent form to combine them effectively.

Learn how to solve a ratio problem involving ratios a:b=5:9 and b:c=4:7. Find the combined ratio a:b:c step-by-step with detailed explanations and examples. Suitable for students in Grades 7-9.

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