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The average (arithmetic mean) of three numbers is 50. If two of the numbers have a sum of 85, what is the third number?
- a)75
- b)70
- c)65
- d)55
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The average (arithmetic mean) of three numbers is 50. If two of the nu...
The average of three numbers is 50: 
Multiply by 3: 150 = a + b + c
Two of the numbers have a sum of 85: 85 = a + b
Substitute into the previous equation: 150 = 85 + c
Subtract 85 to find c: 65 = c
Multiply by 3: 150 = a + b + c
Two of the numbers have a sum of 85: 85 = a + b
Substitute into the previous equation: 150 = 85 + c
Subtract 85 to find c: 65 = c
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The average (arithmetic mean) of three numbers is 50. If two of the nu...
Understanding the Problem
The average of three numbers is given as 50. This means that the total sum of the three numbers can be calculated as follows:
- Total Sum = Average × Number of Items
- Total Sum = 50 × 3 = 150
Identifying Known Values
We are also informed that the sum of two of the numbers is 85. Let's denote the three numbers as A, B, and C, where:
- A + B = 85 (Sum of the first two numbers)
- A + B + C = 150 (Total sum of all three numbers)
Finding the Third Number
To find the third number (C), we can use the total sum of the three numbers:
1. Substitute the sum of A and B in the total sum equation:
- 85 + C = 150
2. Now, isolate C by subtracting 85 from both sides:
- C = 150 - 85
- C = 65
Conclusion
The value of the third number (C) is 65. Thus, the correct answer is option 'C'.
The average of three numbers is given as 50. This means that the total sum of the three numbers can be calculated as follows:
- Total Sum = Average × Number of Items
- Total Sum = 50 × 3 = 150
Identifying Known Values
We are also informed that the sum of two of the numbers is 85. Let's denote the three numbers as A, B, and C, where:
- A + B = 85 (Sum of the first two numbers)
- A + B + C = 150 (Total sum of all three numbers)
Finding the Third Number
To find the third number (C), we can use the total sum of the three numbers:
1. Substitute the sum of A and B in the total sum equation:
- 85 + C = 150
2. Now, isolate C by subtracting 85 from both sides:
- C = 150 - 85
- C = 65
Conclusion
The value of the third number (C) is 65. Thus, the correct answer is option 'C'.
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The average (arithmetic mean) of three numbers is 50. If two of the numbers have a sum of 85, what is the third number?a)75b)70c)65d)55Correct answer is option 'C'. Can you explain this answer?
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