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The product of two numbers is 24 times the difference of these numbers. If the sum of these numbers is 14, find the larger number.
- a)8
- b)56
- c)18
- d)6
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The product of two numbers is 24 times the difference of these numbers...
Xy = 24(x - y) and. x+y = 14
xy = 24x - 24y => x(y - 24) = -24y
=> x= 24y / (24 - y)
24y / (24 - y) +y = 14
24y + 24y - y^2 = 14(24 - y)
48y - y^2 = 336 - 14y
y^2 - 48y - 14y + 336 = 0
y^2 - 62y + 336 = 0
y^2 - 56y - 6y + 336 = 0
y(y - 56) - 6(y - 56) = 0
y=6 or 56
then x=8 or -42
but x>y so x=8.
correct ans - a)8.
xy = 24x - 24y => x(y - 24) = -24y
=> x= 24y / (24 - y)
24y / (24 - y) +y = 14
24y + 24y - y^2 = 14(24 - y)
48y - y^2 = 336 - 14y
y^2 - 48y - 14y + 336 = 0
y^2 - 62y + 336 = 0
y^2 - 56y - 6y + 336 = 0
y(y - 56) - 6(y - 56) = 0
y=6 or 56
then x=8 or -42
but x>y so x=8.
correct ans - a)8.
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Community Answer
The product of two numbers is 24 times the difference of these numbers...
Given information:
- The product of two numbers is 24 times the difference of these numbers.
- The sum of these numbers is 14.
To find: The larger number.
Solution:
Let the two numbers be x and y, where x is the larger number.
From the given information, we can form the following equations:
- xy = 24(x - y) [Product of two numbers is 24 times the difference of these numbers.]
- x + y = 14 [Sum of these numbers is 14.]
Simplifying the first equation, we get:
xy = 24x - 24y
xy - 24x + 24y = 0
x(y - 24) + 24y = 0
x(y - 24) = -24y
Dividing both sides by (y - 24), we get:
x = -24y / (y - 24)
Substituting this value of x in the second equation, we get:
-24y / (y - 24) + y = 14
-24y + y(y - 24) = 14(y - 24)
-24y + y^2 - 24y = 14y - 336
y^2 - 62y + 336 = 0
Solving this quadratic equation, we get:
y = 8 or y = 54
Since x is the larger number, we take y = 8.
Substituting y = 8 in the equation x + y = 14, we get:
x + 8 = 14
x = 6
Therefore, the larger number is x = 6, which is option A.
Answer: A. 6.
- The product of two numbers is 24 times the difference of these numbers.
- The sum of these numbers is 14.
To find: The larger number.
Solution:
Let the two numbers be x and y, where x is the larger number.
From the given information, we can form the following equations:
- xy = 24(x - y) [Product of two numbers is 24 times the difference of these numbers.]
- x + y = 14 [Sum of these numbers is 14.]
Simplifying the first equation, we get:
xy = 24x - 24y
xy - 24x + 24y = 0
x(y - 24) + 24y = 0
x(y - 24) = -24y
Dividing both sides by (y - 24), we get:
x = -24y / (y - 24)
Substituting this value of x in the second equation, we get:
-24y / (y - 24) + y = 14
-24y + y(y - 24) = 14(y - 24)
-24y + y^2 - 24y = 14y - 336
y^2 - 62y + 336 = 0
Solving this quadratic equation, we get:
y = 8 or y = 54
Since x is the larger number, we take y = 8.
Substituting y = 8 in the equation x + y = 14, we get:
x + 8 = 14
x = 6
Therefore, the larger number is x = 6, which is option A.
Answer: A. 6.
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