The sum of three consecutive even integers is 54. What is the smallest integer being added?
A) 8
B) 10
C) 12
D) 16
D . 16
8 + 10 + 12 = ?
10 + 12 + 14 = ?
12 + 14 + 16 = ?
16 + 18 + 20 = ?
To solve this problem, we can use algebra.
Let's assume the first even integer is x.
Since the integers are consecutive, the second even integer would be x + 2, and the third even integer would be x + 4.
The sum of these three numbers is given as 54, so we can write the equation:
x + (x + 2) + (x + 4) = 54
Simplifying the equation:
3x + 6 = 54
Subtracting 6 from both sides:
3x = 48
Dividing both sides by 3:
x = 16
Therefore, the smallest integer being added is 16.
Therefore, the answer is D) 16.
To solve this problem, let's first assign variables to the three consecutive even integers.
Let x be the first even integer. Since the integers are consecutive, the second even integer can be represented as x + 2, and the third even integer can be represented as x + 4.
Since we know that the sum of these three consecutive even integers is 54, we can set up an equation:
x + (x + 2) + (x + 4) = 54
Simplifying the equation, we get:
3x + 6 = 54
Next, we can subtract 6 from both sides of the equation:
3x = 48
Finally, divide both sides by 3:
x = 16
So the first even integer is 16.
Therefore, the smallest integer being added is 16.
The answer is D) 16.