The mean of a set of n numbers is 180, if 54 is added to the set of numbers the new mean is 159. Find n
55
Let's break down the problem step-by-step:
Step 1: Given that the mean of a set of "n" numbers is 180, we can express this algebraically as:
Sum of numbers / n = 180
Step 2: We are also given that if 54 is added to the set of numbers, the new mean becomes 159. This can be expressed as:
(Sum of numbers + 54) / (n + 1) = 159
Step 3: Now we have two equations:
Sum of numbers / n = 180 -- (Equation 1)
(Sum of numbers + 54) / (n + 1) = 159 -- (Equation 2)
Step 4: Let's simplify Equation 1 by multiplying both sides by "n":
Sum of numbers = 180n
Step 5: Next, let's simplify Equation 2:
Sum of numbers + 54 = 159(n + 1)
Sum of numbers + 54 = 159n + 159
Step 6: Move the constant term to the left side of the equation:
Sum of numbers - 159n = -54 + 159
Step 7: Combine like terms:
Sum of numbers - 159n = 105
Step 8: Now, substitute the value from Equation 4 into Equation 7:
180n - 159n = 105
Step 9: Simplify the equation:
21n = 105
Step 10: Solve for "n" by dividing both sides of the equation by 21:
n = 105 / 21
Step 11: Simplify:
n = 5
Therefore, the value of "n" is 5.
To find the value of n, we can use the concept of the mean.
The mean of a set of numbers is calculated by summing all the numbers in the set and then dividing by the total count of numbers in the set.
Let's break down the given information step by step.
Step 1: The mean of a set of n numbers is 180.
This means that the sum of the n numbers is 180n.
Step 2: If 54 is added to the set of numbers, the new mean is 159.
After adding 54 to the numbers, the sum of the n numbers becomes 180n + 54. The count of numbers also increases by 1 to n + 1.
Step 3: Calculate the new mean.
The new mean is 159. So, we can set up the following equation:
(180n + 54) / (n + 1) = 159
Now we can solve this equation to find the value of n.
Multiply both sides of the equation by (n + 1):
180n + 54 = 159(n + 1)
Expand the equation:
180n + 54 = 159n + 159
Simplify the equation:
180n - 159n = 159 - 54
21n = 105
Divide both sides by 21:
n = 105 / 21
Simplify:
n = 5
Therefore, the value of n is 5.
totalbefore=n*180
total after=(n+1)159
but total after is total before+54
total before=n*180
total before+54=(n+1)159
or n*180=(n+1)159 -54
solve for n
n*180-159n=159-54
n=105/21=you do it.