Question
Download Solution PDFThere are three natural numbers. If the average of any two of them is added to the third number, the sum obtained is 175, 183 and 188. What is the average of the three original numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Let the three natural numbers be A, B, and C.
Given conditions:
(A + B)/2 + C = 175
(A + C)/2 + B = 183
(B + C)/2 + A = 188
Concept Used:
Solving the three equations simultaneously to find the values of A, B, and C.
Calculation:
Rewriting the given equations:
⇒ (A + B)/2 + C = 175 ⇒ A + B + 2C = 350 ----(1)
⇒ (A + C)/2 + B = 183 ⇒ A + 2B + C = 366 ----(2)
⇒ (B + C)/2 + A = 188 ⇒ 2A + B + C = 376 ----(3)
Adding all three equations:
⇒ (A + B + 2C) + (A + 2B + C) + (2A + B + C) = 350 + 366 + 376
⇒ 4A + 4B + 4C = 1092
⇒ A + B + C = 273
Average of the three numbers:
⇒ (A + B + C) / 3 = 273 / 3
⇒ 91
∴ The average of the three original numbers is 91.
Last updated on May 29, 2025
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