There are 4 natural numbers. If average of any 3 numbers is added with the fourth, 28, 21,18 or 25 will be obtained. Find the average of the original 4 numbers
Question
There are 4 natural numbers.
If the average of any 3 numbers is added with the fourth, 28, 21, 18 or 25 will be obtained.
Find the average of the original 4 numbers.
Solution
Sure, let's solve this step by step:
Step 1: Let's denote the four numbers as a, b, c, and d.
Step 2: According to the problem, the average of any three numbers added to the fourth gives either 28, 21, 18, or 25. This means:
(a+b+c)/3 + d = 28, (a+b+d)/3 + c = 21, (a+c+d)/3 + b = 18, (b+c+d)/3 + a = 25.
Step 3: Multiply each equation by 3 to simplify:
a+b+c+3d = 84, a+b+3c+d = 63, a+3b+c+d = 54, 3a+b+c+d = 75.
Step 4: Add all four equations together:
6a+6b+6c+6d = 276.
Step 5: Divide the equation by 6:
a+b+c+d = 46.
Step 6: To find the average of the four numbers, divide the sum by 4:
Average = (a+b+c+d)/4 = 46/4 = 11.5.
So, the average of the original four numbers is 11.5.
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