Find three consecutive even numbers such that the difference between 3 times the first number and twice the second number is 1/3 the third number.
also, my teacher told me to use an equation.
Even numbers have a differnce of two.
2, 6, and 8 are consecutive even numbers.
Let n = 1st
Let n + 2 = 2nd
Let n + 4 = 3rd
3(n) - 2(2n+2) = 1/3(n+4)
Here is the equation. Can you solve it?
let n be first number
n+2 be second number
n+4 be third number.
3n-2(n+2)=1/3 * (n+4)
solve for n, then the other numbers.
No JJ, 2,6,8 are not consecutive even numbers. Your equation is wrong.
That isn't the answer. That was just an example of what consecutive even numbers mean to show why we are using n, n+2 and n+4. My equation is the same as yours.
3(n) - 2(2n+2) = 1/3(n+4)
is not the same as
3n-2(n+2)=1/3 * (n+4)
again, 2,6, 8 are not consecutive even numbers.
To find three consecutive even numbers, let's assign a variable to the first number. Let's call it "x". Since the numbers are consecutive even numbers, the second number would be x + 2 (as it follows from adding 2 to get to the next even number), and the third number would be x + 4.
Now let's set up the equation based on the given information. According to the problem statement, the difference between 3 times the first number (3x) and twice the second number (2(x + 2)) is equal to 1/3 the third number [(1/3)(x + 4)].
Putting it all together, the equation will be:
3x - 2(x + 2) = (1/3)(x + 4)
Now we can solve this equation to find the value of x, which will give us the three consecutive even numbers.
Expanding and simplifying the equation:
3x - 2x - 4 = (1/3)(x + 4)
x - 4 = (1/3)(x + 4)
Multiplying both sides of the equation by 3 to eliminate the fraction:
3(x - 4) = x + 4
Expanding and simplifying again:
3x - 12 = x + 4
2x = 16
x = 8
Now that we have found the value of x, we can substitute it back into our expression for the three numbers:
First number = x = 8
Second number = x + 2 = 8 + 2 = 10
Third number = x + 4 = 8 + 4 = 12
Therefore, the three consecutive even numbers are 8, 10, and 12.