Question

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

Answer 1

RU sure?

Answer 2

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 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

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