Find the number that must be subtracted from the terms of the ratio 15 and 19 to make it equal to 3 : 4.

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem of finding the number that must be subtracted from the terms of the ratio 15 and 19 to make it equal to 3:4, we can follow these steps:

### Step 1: Define the variable
Let the number to be subtracted be \( A \).

### Step 2: Set up the equation
After subtracting \( A \) from both terms of the ratio, we can express the new ratio as:
\[ \frac{15 - A}{19 - A} = \frac{3}{4} \]

### Step 3: Cross-multiply
To eliminate the fraction, we will cross-multiply:
\[ 4(15 - A) = 3(19 - A) \]

### Step 4: Expand both sides
Now we expand both sides of the equation:
\[ 60 - 4A = 57 - 3A \]

### Step 5: Rearrange the equation
Next, we will rearrange the equation to isolate \( A \):
\[ 60 - 57 = 4A - 3A \]
This simplifies to:
\[ 3 = A \]

### Step 6: Conclusion
Thus, the number that must be subtracted from the terms of the ratio 15 and 19 to make it equal to 3:4 is:
\[ \boxed{3} \]

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