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If three numbers are added the sum is 15. If the second number is subtracted from the sum of first and third number then we get 5. If twice the first number is added to the second and third number is subtracted from the sum we get 4.Find the three numbers.
- a)1,5,5
- b)2,5,5
- c)3,5,7
- d)4,3,5
Correct answer is option 'C'. Can you explain this answer?
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If three numbers are added the sum is 15. If the second number is sub...
Let a, b, c be the three numbers
View all questions of this test
Given a + b + c = 15.....(i)
(a + c) − b = 5.....(ii)
(2a + b) − c = 4......(iii)
a + b + c = 15.........(i)
a − b + c = 5.......(ii)
2a + b − c = 4......(iii)
(1)+(2) ⇒ a + b + c + a − b + c = 15 + 5
2a + 2c = 20 (or) a + b = 10......(iv)
substituting (4) in (1) ⇒ b + (a + c) = 15
⇒ b + 10 = 15
⇒ b = 15 − 10 = 5
equation (1) + equation (3)
⇒ a + b + c + 2a + b − x = 15 + 4
⇒ 3a + 2b = 19 ⇒ 3a = 19 − 2b
⇒ 3a = 19 − 2(5)
⇒ 3a = 19 − 10 = 9
∴ a = 9/3 = 3
∴ a = 3, b = 5
put a = 3, b = 5 in
(1) we get
3 + 5 + = 15
Most Upvoted Answer
If three numbers are added the sum is 15. If the second number is sub...
Given information:
- Three numbers are added and the sum is 15.
- The second number is subtracted from the sum of the first and third number, resulting in 5.
- Twice the first number is added to the second number and the third number is subtracted from the sum, resulting in 4.
To find:
The three numbers that satisfy these conditions.
Solution:
Let's assume the three numbers as follows:
- First number = x
- Second number = y
- Third number = z
Condition 1: Three numbers are added and the sum is 15.
x + y + z = 15
Condition 2: The second number is subtracted from the sum of the first and third number, resulting in 5.
(x + z) - y = 5
Condition 3: Twice the first number is added to the second number and the third number is subtracted from the sum, resulting in 4.
2x + y - z = 4
Now, let's solve these equations to find the values of x, y, and z.
Solving the equations:
Equation 1: x + y + z = 15
Equation 2: (x + z) - y = 5
Equation 3: 2x + y - z = 4
Rearranging Equation 2, we get:
x + z - y = 5
Adding Equation 1 and Equation 2, we eliminate y:
(x + y + z) + (x + z - y) = 15 + 5
2x + 2z = 20
Dividing by 2 on both sides, we get:
x + z = 10
Substituting this value in Equation 3, we get:
2x + y - z = 4
2x + y - (10 - x) = 4
2x + y - 10 + x = 4
3x + y = 14
Now, we have two equations:
x + z = 10
3x + y = 14
Solving these equations simultaneously, we find:
x = 3
y = 5
z = 7
Therefore, the three numbers are 3, 5, and 7.
Hence, option C) 3, 5, 7 is the correct answer.
- Three numbers are added and the sum is 15.
- The second number is subtracted from the sum of the first and third number, resulting in 5.
- Twice the first number is added to the second number and the third number is subtracted from the sum, resulting in 4.
To find:
The three numbers that satisfy these conditions.
Solution:
Let's assume the three numbers as follows:
- First number = x
- Second number = y
- Third number = z
Condition 1: Three numbers are added and the sum is 15.
x + y + z = 15
Condition 2: The second number is subtracted from the sum of the first and third number, resulting in 5.
(x + z) - y = 5
Condition 3: Twice the first number is added to the second number and the third number is subtracted from the sum, resulting in 4.
2x + y - z = 4
Now, let's solve these equations to find the values of x, y, and z.
Solving the equations:
Equation 1: x + y + z = 15
Equation 2: (x + z) - y = 5
Equation 3: 2x + y - z = 4
Rearranging Equation 2, we get:
x + z - y = 5
Adding Equation 1 and Equation 2, we eliminate y:
(x + y + z) + (x + z - y) = 15 + 5
2x + 2z = 20
Dividing by 2 on both sides, we get:
x + z = 10
Substituting this value in Equation 3, we get:
2x + y - z = 4
2x + y - (10 - x) = 4
2x + y - 10 + x = 4
3x + y = 14
Now, we have two equations:
x + z = 10
3x + y = 14
Solving these equations simultaneously, we find:
x = 3
y = 5
z = 7
Therefore, the three numbers are 3, 5, and 7.
Hence, option C) 3, 5, 7 is the correct answer.
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If three numbers are added the sum is 15. If the second number is subtracted from the sum of first and third number then we get 5. If twice the first number is added to the second and third number is subtracted from the sum we get 4.Find the three numbers.a)1,5,5b)2,5,5c)3,5,7d)4,3,5Correct answer is option 'C'. Can you explain this answer?
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