What must be added to each term of the ratio `3 : 5` so that the new ratio becomes `5 : 6`?

Options

A. 6
B. 7
C. 8
D. 5

Answer

To solve the problem of what must be added to each term of the ratio \(3 : 5\) so that the new ratio becomes \(5 : 6\), we can follow these steps:

### Step 1: Define the variable
Let \(x\) be the number that we need to add to each term of the ratio \(3 : 5\).

### Step 2: Write the new ratio
After adding \(x\) to each term, the new ratio will be \((3 + x) : (5 + x)\).

### Step 3: Set up the equation
According to the problem, this new ratio should equal \(5 : 6\). Therefore, we can write the equation:
\[ \frac{3 + x}{5 + x} = \frac{5}{6} \]

### Step 4: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 6(3 + x) = 5(5 + x) \]

### Step 5: Expand both sides
Expanding both sides, we get:
\[ 18 + 6x = 25 + 5x \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to isolate \(x\):
\[ 6x - 5x = 25 - 18 \]
This simplifies to:
\[ x = 7 \]

### Conclusion
Thus, the number that must be added to each term of the ratio \(3 : 5\) to make the new ratio \(5 : 6\) is \(7\).

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