Find two consecutive even integers such that six times the lesser added to the greater gives a sum of 86

Answer 1

Let the two consecutive even integers be represented as \( x \) (the lesser integer) and \( x + 2 \) (the greater integer).

According to the problem, we can set up the following equation based on the condition given:

\[ 6x + (x + 2) = 86 \]

Now, we simplify the equation:

\[ 6x + x + 2 = 86 \]

Combine like terms:

\[ 7x + 2 = 86 \]

Next, subtract 2 from both sides to isolate the term with \( x \):

\[ 7x = 86 - 2 \]

\[ 7x = 84 \]

Now, divide both sides by 7 to solve for \( x \):

\[ x = \frac{84}{7} = 12 \]

Now that we have the value of \( x \), we can find the two consecutive even integers:

The lesser integer is \( x = 12 \), and the greater integer is:

\[ x + 2 = 12 + 2 = 14 \]

Thus, the two consecutive even integers are \( 12 \) and \( 14 \).

To verify, we can check the original condition:

Calculate \( 6 \times 12 + 14 \):

\[ 6 \times 12 = 72 \] \[ 72 + 14 = 86 \]

Since our calculation holds true, the solution is confirmed. Therefore, the two consecutive even integers are

\[ \boxed{12} \text{ and } \boxed{14}. \]

Answer 2

RU sure?

Answer 3

Yes, let's go through the solution again step by step to ensure accuracy.

We want to find two consecutive even integers such that six times the lesser added to the greater gives a sum of 86.

Step 1: Define the integers. Let the lesser even integer be \( x \). Therefore, the next consecutive even integer would be \( x + 2 \).

Step 2: Set up the equation. According to the problem, we need to set up the equation based on the condition provided:

\[ 6x + (x + 2) = 86 \]

Step 3: Simplify the equation. Combine the terms:

\[ 6x + x + 2 = 86 \]

This simplifies to:

\[ 7x + 2 = 86 \]

Step 4: Solve for \( x \). Subtract 2 from both sides:

\[ 7x = 86 - 2 \]

\[ 7x = 84 \]

Now, divide both sides by 7:

\[ x = \frac{84}{7} = 12 \]

Step 5: Find the two integers. The lesser integer is \( x = 12 \), and the greater integer is:

\[ x + 2 = 12 + 2 = 14 \]

Step 6: Verify the solution. Now let's check whether the condition is satisfied:

Calculate \( 6 \times 12 + 14 \):

\[ 6 \times 12 = 72 \] \[ 72 + 14 = 86 \]

Since the left-hand side equals the right-hand side, our solution is indeed correct.

Therefore, the two consecutive even integers are

\[ \boxed{12} \text{ and } \boxed{14}. \]