The average of five number is 56. Four of the numbers are the same. The average of one of the four number and the fifth number is 80. What is the fifth number.
56*5=280
80*2=160
280-160=120
5/120=24
Is 24 correct?
No. Shouldn't the 120 be divided by three?
40,40,40,40,120 it seems to me.
That makes sense I need to leave out the 1st and the fifth number and use just the three numbers that are not calculated. Bob you are a life saver thank you.
To find the fifth number, let's first find the sum of the five numbers.
The average of the five numbers is 56, so multiplying 56 by 5 gives us the sum of the five numbers, which is 280.
Next, we are given that four of the numbers are the same. So, let's call this common number "x." Since there are four identical numbers, the sum of these four identical numbers will be 4x.
We are also given that the average of one of the four identical numbers and the fifth number is 80. This means that the sum of one of the four identical numbers and the fifth number is 80 * 2 = 160.
Now, using the information we have, we can set up an equation:
(4x + Fifth Number) = 160
Since we know the sum of the five numbers is 280, we can write another equation:
4x + Fifth Number = 280
Now we have a system of equations:
4x + Fifth Number = 280
4x + Fifth Number = 160
To solve this system, we need to subtract the second equation from the first equation:
(4x + Fifth Number) - (4x + Fifth Number) = 280 - 160
0 = 120
This means that there is no solution to our system of equations. Therefore, there is no specific value we can assign to the fifth number. The fifth number could be any value, and 24 is not necessarily the correct answer.