If `(a)/(3) = (b)/(8)`, then `(a + 3) : (b + 8)` is equal to

Options

A. `3 :8`
B. `8 ,3`
C. `5 : 8`
D. `3 : 5`

Answer

To solve the problem, we start with the given equation:

\[ \frac{a}{3} = \frac{b}{8} \]

### Step 1: Cross-multiply to find a relationship between a and b.

Cross-multiplying gives us:

\[ 8a = 3b \]

### Step 2: Express a and b in terms of a common variable.

Let’s express \(a\) and \(b\) in terms of a common variable \(k\). We can write:

\[ a = 3k \quad \text{and} \quad b = 8k \]

### Step 3: Substitute a and b into the expression \((a + 3) : (b + 8)\).

Now we substitute \(a\) and \(b\) into the expression \((a + 3) : (b + 8)\):

\[ (a + 3) = (3k + 3) = 3(k + 1) \]

\[ (b + 8) = (8k + 8) = 8(k + 1) \]

### Step 4: Write the ratio.

Now we can write the ratio:

\[ \frac{a + 3}{b + 8} = \frac{3(k + 1)}{8(k + 1)} \]

### Step 5: Simplify the ratio.

Since \(k + 1\) is common in both the numerator and the denominator, we can cancel it out (assuming \(k + 1 \neq 0\)):

\[ \frac{3(k + 1)}{8(k + 1)} = \frac{3}{8} \]

### Final Answer:

Thus, the ratio \((a + 3) : (b + 8)\) is equal to:

\[ 3 : 8 \]

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