Answer :
Therefore,the values of x and y are 8 and 7, respectively.
To find the values of x and y, let's first calculate the mean of the five numbers:
Mean = Sum of all numbers / Total number of numbers
The sum of the five numbers is 5 + 8 + x + y + 12, and since there are five numbers, the mean is:
Mean = (5 + 8 + x + y + 12) / (5)
Now, since the mean and the median are the same, the median will be the middle value when the numbers are arranged in ascending order.
The median of 5,8,x,y,12 will be the third number when arranged in ascending order. Since the numbers are written in order, x will be the third number.
Therefore, the median (which is also the mean) will be:
Median = (x+8) / 2
Since the mean and median are the same:
(5 + 8 + x + y + 12) / (5) = (x+8) / 2
Now, we can solve this equation for x and y:
(25 + x + y) / 5 = (x+8) / 2
Cross multiplying:
2(25 + x + y) = 5(x + 8)
50 + 2x +2y = 5x + 40
2x + 2y = 5x − 10
2y = 3x − 10
y = (3x − 10) / 2
Now, we need to find the value of x and y such that x is the third number and the mean and median are equal. To achieve this, let's equate x to the median:
x = (x+8) / 2
Solving for x:
2x = x + 8
x = 8
Now, substitute x=8 into the equation for y:
y = (3(8)−10) / 2
y = (24−10) / 2
y = 7
Complete Question:
Five whole numbers are written in order. 5,8,x,y,12 The mean and median of the five numbers are the same. Work out the values of x and y.
