What number has to be added to each term of `3 : 5` to make the ratio `5 : 6`

Options

A. 6
B. 9
C. 12
D. 11

Answer

To solve the problem of what number needs to be added to each term of the ratio \(3 : 5\) to make it equal to the ratio \(5 : 6\), we can follow these steps:

### Step 1: Define the unknown
Let \(x\) be the number that we need to add to both terms of the ratio \(3 : 5\).

### Step 2: Set up the equation
After adding \(x\) to both terms, the new ratio becomes \((3 + x) : (5 + x)\). We want this ratio to equal \(5 : 6\). Therefore, we can set up the equation:
\[ \frac{3 + x}{5 + x} = \frac{5}{6} \]

### Step 3: Cross-multiply to eliminate the fraction
To solve the equation, we can cross-multiply:
\[ 6(3 + x) = 5(5 + x) \]

### Step 4: Distribute on both sides
Now, we will distribute the numbers:
\[ 18 + 6x = 25 + 5x \]

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

### Step 6: Conclusion
The number that needs to be added to each term of the ratio \(3 : 5\) to make it equal to \(5 : 6\) is \(7\).