Question

Given three consecutive even integers whose sum is 54, find the largest of the three integers.

Answer 1

The largest of the three numbers is 20

Explanation:

16, 18, 20

(n) + n+2 + n+4

Note:

We only took even numbers

Answer 2

20

Explanation:

Let the least integer = x. The three consecutive even integers can be denoted as:

x , x + 2 , x + 4

Set the equation:

(x) + (x + 2) + (x + 4) = 54

Simplify. Combine like terms:

(x + x + x) + (2 + 4) = 54

(3x) + (6) = 54

3x + 6 = 54

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

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First, subtract 6 from both sides of the equation:

3x + 6 (-6) = 54 (-6)

3x = 54 - 6

3x = 48

Next, divide 3 from both sides of the equation:

(3x)/3 = (48)/3

x = 48/3

x = 16

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Next, find the largest of the three integers, which was denoted as x + 4:

x + 4

(16) + 4 = 20

20 is the largest integer.

Check:

x + (x + 2) + (x + 4) = 54

16 + (16 + 2) + (16 + 4) = 54

16 + 18 + 20 = 54

16 + 38 = 54

54 = 54 (True).

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