Answer :
Answer:
Okay, let's approach this step by step:
In a set of numbers, the mean is the sum of all numbers divided by the count of numbers.
In a set with an odd number of numbers (like this one with 5 numbers), the median is the middle number when the numbers are arranged in order.
We are told that the mean and median are the same. This means that x must be the median, as it's the middle number in the ordered list.
Let's call the mean (and median) M. Then:
$7 + 7 + x + y + 9 = 5M$
Simplify:
$23 + x + y = 5M$
We know that x is the median, so:
$x = M$
Substitute this into the equation from step 5:
$23 + M + y = 5M$
Simplify:
$23 + y = 4M$
We are looking for whole numbers. The smallest possible value for M that makes the left side divisible by 4 is 7. Let's try that:
If $M = 7$, then $x = 7$ (because x = M)
Substituting M = 7 into the equation from step 8:
$23 + y = 4(7)$
$23 + y = 28$
$y = 5$
Check: If the numbers are 7, 7, 7, 5, 9, then:
Mean = $(7 + 7 + 7 + 5 + 9) / 5 = 35 / 5 = 7$
Median = 7
Mean = Median, so this works.
Therefore, $x = 7$ and $y = 5$.
