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There are two numbers such that the first number is half of the second number. If their average is 57, then what is the first number?
- a)19
- b)38
- c)21
- d)29
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are two numbers such that the first number is half of the second...
GIVEN:
Average of two numbers = 57
Average of two numbers = 57
FORMULA USED:
Average of two numbers (a, b) = (a + b)/2
Average of two numbers (a, b) = (a + b)/2
CALCULATION:
Let the first number be ‘x’
⇒ Second number = 2x
Now, average = 57
⇒ (x + 2x)/2 = 57
⇒ 3x = 114
⇒ x = 114/3 = 38
∴ The first number is 38
Let the first number be ‘x’
⇒ Second number = 2x
Now, average = 57
⇒ (x + 2x)/2 = 57
⇒ 3x = 114
⇒ x = 114/3 = 38
∴ The first number is 38
Most Upvoted Answer
There are two numbers such that the first number is half of the second...
Given:
- There are two numbers, let's call them x and y.
- The first number is half of the second number, which can be written as x = y/2.
- The average of the two numbers is 57.
To find the first number, we need to solve the given information.
1. Find the relationship between the two numbers
- We are given that the first number is half of the second number, so we can write x = y/2.
2. Find the average of the two numbers
- The average of two numbers is the sum of the numbers divided by 2.
- Since we are given that the average is 57, we can write (x + y)/2 = 57.
3. Substitute the value of x from the first equation into the second equation
- Replace x with y/2 in the second equation: (y/2 + y)/2 = 57.
4. Simplify the equation
- Multiply both sides of the equation by 2 to eliminate the fraction: y + 2y = 4 * 57.
- Combine like terms: 3y = 228.
5. Solve for y
- Divide both sides of the equation by 3: y = 76.
6. Find the value of x
- Substitute the value of y back into the first equation: x = 76/2.
- Simplify: x = 38.
Therefore, the first number is 38.
- There are two numbers, let's call them x and y.
- The first number is half of the second number, which can be written as x = y/2.
- The average of the two numbers is 57.
To find the first number, we need to solve the given information.
1. Find the relationship between the two numbers
- We are given that the first number is half of the second number, so we can write x = y/2.
2. Find the average of the two numbers
- The average of two numbers is the sum of the numbers divided by 2.
- Since we are given that the average is 57, we can write (x + y)/2 = 57.
3. Substitute the value of x from the first equation into the second equation
- Replace x with y/2 in the second equation: (y/2 + y)/2 = 57.
4. Simplify the equation
- Multiply both sides of the equation by 2 to eliminate the fraction: y + 2y = 4 * 57.
- Combine like terms: 3y = 228.
5. Solve for y
- Divide both sides of the equation by 3: y = 76.
6. Find the value of x
- Substitute the value of y back into the first equation: x = 76/2.
- Simplify: x = 38.
Therefore, the first number is 38.
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