The sum of 5 consecutive even numbers A,B,C,D and E is 130. What is the product of A and E?

Options

A. 720
B. 616
C. 660
D. 672

Answer

To solve the problem step by step, we will find the five consecutive even numbers whose sum is 130 and then calculate the product of the first and the last number.

### Step 1: Define the consecutive even numbers
Let the first even number be \( A \). Since we are dealing with consecutive even numbers, we can express the five numbers as:
- \( A \) (first even number)
- \( B = A + 2 \) (second even number)
- \( C = A + 4 \) (third even number)
- \( D = A + 6 \) (fourth even number)
- \( E = A + 8 \) (fifth even number)

### Step 2: Set up the equation for their sum
According to the problem, the sum of these five numbers is 130:
\[ A + B + C + D + E = 130 \]
Substituting the expressions for \( B, C, D, \) and \( E \):
\[ A + (A + 2) + (A + 4) + (A + 6) + (A + 8) = 130 \]

### Step 3: Simplify the equation
Combine like terms:
\[ A + A + 2 + A + 4 + A + 6 + A + 8 = 130 \]
This simplifies to:
\[ 5A + 20 = 130 \]

### Step 4: Solve for \( A \)
Now, isolate \( A \):
\[ 5A = 130 - 20 \]
\[ 5A = 110 \]
\[ A = \frac{110}{5} = 22 \]

### Step 5: Find the values of \( B, C, D, \) and \( E \)
Now that we have \( A \), we can find the other numbers:
- \( B = A + 2 = 22 + 2 = 24 \)
- \( C = A + 4 = 22 + 4 = 26 \)
- \( D = A + 6 = 22 + 6 = 28 \)
- \( E = A + 8 = 22 + 8 = 30 \)

### Step 6: Calculate the product of \( A \) and \( E \)
Now we need to find the product of \( A \) and \( E \):
\[ A \times E = 22 \times 30 \]
Calculating this gives:
\[ A \times E = 660 \]

### Final Answer
The product of \( A \) and \( E \) is \( 660 \).

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