the mean of five numbers is 20. the mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number
3*16 + x + x+8 = 5*20
so now just solve for x and then x+8
x=22 so x plus 8 =30
34 since 20*5=100
16*3=48
52/2=26+8=34
Why did the fifth number go to the psychiatrist? Because it couldn't stop comparing itself to the fourth number and needed professional help!
Let's take a closer look at the problem.
We know that the mean of the five numbers is 20. So, if we add up all five numbers and divide by 5, we get a total of 20. This gives us:
(x + y + z + w + f)/5 = 20
We also know that the mean of the first three numbers (x, y, and z) is 16:
(x + y + z)/3 = 16
Finally, we know that the fifth number (f) is greater than the fourth number (w) by 8:
f = w + 8
Now, let's use these equations to find the fifth number.
From the second equation, we can express one of the variables in terms of the others. Let's use z:
z = 48 - x - y
Substituting this expression for z into the first equation:
(x + y + (48 - x - y) + w + f)/5 = 20
Simplifying this equation:
(48 + w + f)/5 = 20
Multiplying both sides by 5:
48 + w + f = 100
Now, let's use the third equation to find the fifth number:
f = w + 8
Substituting this expression for f into the previous equation:
48 + w + w + 8 = 100
Combining like terms:
2w + 56 = 100
Subtracting 56 from both sides:
2w = 44
Dividing both sides by 2:
w = 22
And finally, substituting the value of w into the equation for f:
f = 22 + 8
f = 30
So, the fifth number is 30.
To find the fifth number, we need to first find the sum of the five numbers.
Given that the mean of the five numbers is 20, we know that the sum of the five numbers is 20 multiplied by 5, which gives us 100.
Next, we are given that the mean of the first three numbers is 16. This means that the sum of the first three numbers is 16 multiplied by 3, which gives us 48.
Now, we know that the sum of the first three numbers is 48. To find the sum of the fourth and fifth numbers, we subtract 48 from the total sum of the five numbers (100 - 48 = 52).
We are also given that the fifth number is greater than the fourth by 8. So, if we let the fourth number be x, then the fifth number would be x + 8.
To find the sum of the fourth and fifth numbers, we add x and x + 8, which gives us 2x + 8.
We know that the sum of the fourth and fifth numbers is 52, so we can set up the equation:
2x + 8 = 52
Simplifying the equation, we subtract 8 from both sides:
2x = 44
Then, we divide both sides of the equation by 2:
x = 22
Therefore, the fourth number is 22. Since the fifth number is greater than the fourth by 8, the fifth number is:
22 + 8 = 30
So, the fifth number is 30.