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The sum of the two numbers is 30. Four times one number is one more than three times the other number. Find the larger number.
- a)13
- b)17
- c)18
- d)12
Correct answer is option 'B'. Can you explain this answer?
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The sum of the two numbers is 30. Four times one number is one more th...
GIVEN:
Sum of two numbers = 30
4 × first number = 3 × second number
Sum of two numbers = 30
4 × first number = 3 × second number
CALCULATION:
let the two number be a and b.
a + b = 30 …(i)
4a = 3b + 1
4a – 3b = 1 …(ii)
Multiplying (i) by 3 and add (ii)
3a + 3b = 90
4a – 3b = 1
We get, a = 13 and b = 17
∴ Larger number is 17.
let the two number be a and b.
a + b = 30 …(i)
4a = 3b + 1
4a – 3b = 1 …(ii)
Multiplying (i) by 3 and add (ii)
3a + 3b = 90
4a – 3b = 1
We get, a = 13 and b = 17
∴ Larger number is 17.
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The sum of the two numbers is 30. Four times one number is one more th...
To solve this problem, we can use algebraic equations. Let's assume that the two numbers are x and y.
Given information:
1) The sum of the two numbers is 30: x + y = 30
2) Four times one number is one more than three times the other number: 4x = 3y + 1
To find the larger number, we need to compare the values of x and y. Let's solve the above equations to determine their values.
- Solving the first equation for x:
x = 30 - y
- Substituting this value of x in the second equation:
4(30 - y) = 3y + 1
120 - 4y = 3y + 1
- Simplifying the equation:
120 - 1 = 3y + 4y
119 = 7y
y = 17
Now that we have found the value of y, we can substitute it back into the first equation to find the value of x.
- Substituting y = 17 in the first equation:
x + 17 = 30
x = 30 - 17
x = 13
So, the two numbers are 13 and 17. To find the larger number, we compare the values of x and y.
- Comparing x = 13 and y = 17:
Since 17 is greater than 13, the larger number is 17.
Therefore, the correct answer is option B) 17.
Given information:
1) The sum of the two numbers is 30: x + y = 30
2) Four times one number is one more than three times the other number: 4x = 3y + 1
To find the larger number, we need to compare the values of x and y. Let's solve the above equations to determine their values.
- Solving the first equation for x:
x = 30 - y
- Substituting this value of x in the second equation:
4(30 - y) = 3y + 1
120 - 4y = 3y + 1
- Simplifying the equation:
120 - 1 = 3y + 4y
119 = 7y
y = 17
Now that we have found the value of y, we can substitute it back into the first equation to find the value of x.
- Substituting y = 17 in the first equation:
x + 17 = 30
x = 30 - 17
x = 13
So, the two numbers are 13 and 17. To find the larger number, we compare the values of x and y.
- Comparing x = 13 and y = 17:
Since 17 is greater than 13, the larger number is 17.
Therefore, the correct answer is option B) 17.
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