Answer:
The three numbers are 14, 16, 18.
Step-by-step explanation:
Consecutive even integers differ by 2.
You can let the smallest of the three numbers equal x. Then the other two numbers are x + 2 and x + 4.
Now use x, x + 2,and x + 4 to represent the 3 numbers and follow the directions to write an equation. The equation will have only one variable, x, so you can solve for x.
"four times the first" -----> 4x
"minus the third" -------> -(x + 4)
"is" -----> =
"six more than twice the second" ------> 2(x + 2) + 6
Put all the pieces in boldface together to arrive at your equation.
4x - (x + 4) = 2(x + 2) + 6
Simplify the parentheses on both sides by distributing.
4x - x - 4 = 2x + 4 + 6
Combine like terms on both sides.
3x - 4 = 2x + 10
Subtract 2x from both sides.
x - 4 = 10
Add 4 to both sides.
x = 14
The smallest number is 14.
x + 2 = 14 + 2 = 16
x + 4 = 14 + 4 = 18
Answer: The three numbers are 14, 16, 18.
