u : v = 4 : 7 and v : w = 9 : 7. If u = 72, then what is the value of w ?

Options

A. 98
B. 77
C. 63
D. 49

Answer

To solve the problem step by step, we will use the given ratios and the value of \( u \) to find the value of \( w \).

### Step 1: Understand the Ratios
We are given two ratios:
1. \( u : v = 4 : 7 \)
2. \( v : w = 9 : 7 \)

### Step 2: Express \( v \) in terms of \( u \)
From the first ratio \( u : v = 4 : 7 \), we can express \( v \) in terms of \( u \):
\[ \frac{u}{v} = \frac{4}{7} \implies v = \frac{7}{4} u \]

### Step 3: Substitute the value of \( u \)
We know that \( u = 72 \). Substitute this value into the equation for \( v \):
\[ v = \frac{7}{4} \times 72 \]

### Step 4: Calculate \( v \)
Now, calculate \( v \):
\[ v = \frac{7 \times 72}{4} = \frac{504}{4} = 126 \]

### Step 5: Express \( w \) in terms of \( v \)
From the second ratio \( v : w = 9 : 7 \), we can express \( w \) in terms of \( v \):
\[ \frac{v}{w} = \frac{9}{7} \implies w = \frac{7}{9} v \]

### Step 6: Substitute the value of \( v \)
Now substitute the value of \( v \) we calculated:
\[ w = \frac{7}{9} \times 126 \]

### Step 7: Calculate \( w \)
Now, calculate \( w \):
\[ w = \frac{7 \times 126}{9} = \frac{882}{9} = 98 \]

### Final Answer
Thus, the value of \( w \) is \( 98 \).