The average of 7 consecutive whole numbers is 7. Then 1 is added to the first number, 2 is added to the second number, 3 is added to the third number, and so on. What is the average of the seven new numbers? Use the variable n to solve. Let n be the first number.
Let's use the variable n to represent the first number.
The seven consecutive whole numbers can be represented as: n, n+1, n+2, n+3, n+4, n+5, n+6.
We know that the average of these numbers is 7, so:
(n + n+1 + n+2 + n+3 + n+4 + n+5 + n+6) / 7 = 7
Multiplying both sides of the equation by 7 gives us:
7n + 7(n+1) + 7(n+2) + 7(n+3) + 7(n+4) + 7(n+5) + 7(n+6) = 7 * 7
Simplifying both sides of the equation gives us:
7n + 7n + 7 + 14n + 21 + 21n + 42 + 28n + 49 + 35n + 70 + 42n + 84 = 49
Combine like terms:
147n + 273 = 49
Subtract 273 from both sides of the equation:
147n = 49 - 273
147n = -224
Now, divide both sides of the equation by 147:
n = -224 / 147
Simplifying the fraction gives us:
n ≈ -1.52
Therefore, the first number is approximately -1.52.
Adding 1, 2, 3, 4, 5, 6, and 7 respectively to each of the numbers n, n+1, n+2, n+3, n+4, n+5, n+6, we get:
n = -1.52
n+1 = -0.52
n+2 = 0.48
n+3 = 1.48
n+4 = 2.48
n+5 = 3.48
n+6 = 4.48
The average of these numbers can be calculated by adding them together and dividing by 7:
(-1.52 + -0.52 + 0.48 + 1.48 + 2.48 + 3.48 + 4.48) / 7
= (10.88) / 7
= 1.55 (rounded to two decimal places)
Therefore, the average of the seven new numbers is approximately 1.55.