One number is n and a second number is (⅔ n + 2). A third number is ⅙ n less than the second number. Express the sum of the three numbers in terms of n.
clearly, n + (⅔ n + 2) + (⅔ n + 2) - 1/6 n
so, what is 1+⅔+⅔-1/6 ? 2+2=?
n + 2n/3 + 2 + 2 n/3 + 2 - n/6
4 + n +8n/6 - n/6
4 + 6n/6 + 8n/6 - n/6
4 + 13 n/6
To find the sum of the three numbers in terms of n, let's break down the problem step by step.
Step 1: Define the numbers
The first number is given as n.
The second number is (2/3)n + 2.
The third number is (2/3)n + 2 - (1/6)n.
Step 2: Simplify the expression
To find the sum, we need to add all three numbers together.
Sum = n + (2/3)n + 2 + (2/3)n + 2 - (1/6)n.
Step 3: Combine like terms
To simplify the expression further, we can add the coefficients of the like terms.
Sum = n + (2/3 + 2/3)n - (1/6)n + 2 + 2.
Step 4: Calculate the sum
Let's add all the terms together:
Sum = n + (4/3)n - (1/6)n + 4.
To combine the coefficients, we need a common denominator, which is 6.
Sum = (6/6)n + (8/6)n - (1/6)n + 4.
Now, sum the coefficients:
Sum = (13/6)n + 4.
Therefore, the sum of the three numbers in terms of n is (13/6)n + 4.