Questions: A 1 Quiz Review 2-5, 2-6, 2-7-8 HONORS 19. The sum of three consecutive even numbers is 90. Find the numbers. Equation: Smallest: Middle: Largest:

Solution Steps

To solve the problem of finding three consecutive even numbers whose sum is 90, we can use algebra. Let's denote the smallest of these numbers as \( x \). The next consecutive even number would be \( x + 2 \), and the largest would be \( x + 4 \). The sum of these three numbers is given by the equation \( x + (x + 2) + (x + 4) = 90 \). We can solve this equation to find \( x \) and then determine the three numbers.

1. Define the smallest number as \( x \).
2. Express the middle and largest numbers in terms of \( x \).
3. Set up the equation for the sum of these numbers.
4. Solve the equation for \( x \).
5. Calculate the three consecutive even numbers.

Let the smallest of the three consecutive even numbers be \( x \). The next two consecutive even numbers can be expressed as \( x + 2 \) and \( x + 4 \).

The sum of the three consecutive even numbers is given by: \[ x + (x + 2) + (x + 4) = 90 \]

Combine like terms: \[ 3x + 6 = 90 \]

Isolate \( x \) by first subtracting 6 from both sides: \[ 3x = 84 \] Then, divide both sides by 3: \[ x = 28 \]

Using \( x = 28 \), the three consecutive even numbers are: \[ \text{Smallest: } x = 28 \] \[ \text{Middle: } x + 2 = 30 \] \[ \text{Largest: } x + 4 = 32 \]

Final Answer