A is 20 years older than B. 5 years ago, A was 3 times as old as B. Find their present ages.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the Variables
Let:
- A = present age of person A
- B = present age of person B

### Step 2: Set Up the Equations
From the problem statement, we have two pieces of information:
1. A is 20 years older than B.
2. Five years ago, A was three times as old as B.

From the first statement, we can write the equation:
\[ A = B + 20 \] (Equation 1)

From the second statement, we can express the ages five years ago:
- Age of A five years ago: \( A - 5 \)
- Age of B five years ago: \( B - 5 \)

According to the second statement:
\[ A - 5 = 3(B - 5) \] (Equation 2)

### Step 3: Substitute Equation 1 into Equation 2
Now, we will substitute Equation 1 into Equation 2:
\[ (B + 20) - 5 = 3(B - 5) \]

This simplifies to:
\[ B + 15 = 3B - 15 \]

### Step 4: Rearrange the Equation
Now, let's rearrange the equation to isolate B:
\[ B + 15 + 15 = 3B \]
\[ B + 30 = 3B \]

Subtract B from both sides:
\[ 30 = 3B - B \]
\[ 30 = 2B \]

### Step 5: Solve for B
Now, divide both sides by 2:
\[ B = \frac{30}{2} \]
\[ B = 15 \]

### Step 6: Solve for A
Now that we have B, we can find A using Equation 1:
\[ A = B + 20 \]
\[ A = 15 + 20 \]
\[ A = 35 \]

### Conclusion
The present ages are:
- A = 35 years
- B = 15 years