The following four numbers are listed in ascending order: 7, x, 24, y. the median of the four numbers is 18 and the mean is 61. Find y x=12

If the median is 18

then 18 is halfway between x and 24
18 = (x+24)/2
x+24 = 36
x = 12
so we have
7 , 12 , 24 , y

well 61 = 7+12+24+y /4
244 = 43 + y
y = 201

To find the value of y, we can use the given information about the median and the mean of the four numbers.

Step 1: Determine the median
The median is the middle number when the numbers are arranged in ascending order. In this case, we know that the median is 18. Since x is the number that comes after 7 and before 24, the value of x must be the median. Therefore, x = 18.

Step 2: Calculate the sum of the four numbers
To find the mean, we need to calculate the sum of all the numbers and divide by 4 (since we have four numbers).

Sum of the four numbers = 7 + x + 24 + y
Sum of the four numbers = 7 + 18 + 24 + y (substituting x = 18 from Step 1)

Step 3: Calculate the mean
We are given that the mean is 61. Therefore, the mean of the four numbers can be calculated as:

Mean = (Sum of the four numbers) / 4
61 = (7 + 18 + 24 + y) / 4

Step 4: Solve for y
To find the value of y, we can rearrange the equation and solve for y:

61 * 4 = 7 + 18 + 24 + y
244 = 49 + y
y = 244 - 49
y = 195

Therefore, the value of y is 195.