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A fraction becomes 9/11, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and denominator it becomes 5/6, then the fraction is
- a)9/7
- b)-9/7
- c)7/9
- d)-7/9
Correct answer is option 'C'. Can you explain this answer?
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A fraction becomes9/11, if 2 is added to both the numerator and denomi...
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A fraction becomes9/11, if 2 is added to both the numerator and denomi...
To solve this problem, we need to set up a system of equations using the given information.
Let's assume the original fraction is x/y.
According to the problem, when 2 is added to both the numerator and denominator, the fraction becomes 9/11. This can be represented by the equation:
(x + 2) / (y + 2) = 9/11
Similarly, when 3 is added to both the numerator and denominator, the fraction becomes 5/6. This can be represented by the equation:
(x + 3) / (y + 3) = 5/6
We now have a system of two equations with two variables. We can solve this system to find the values of x and y.
Solving the System of Equations:
- Multiply both sides of the first equation by (y + 2) and the second equation by (y + 3) to eliminate the denominators:
11(x + 2) = 9(y + 2)
6(x + 3) = 5(y + 3)
- Simplify and expand:
11x + 22 = 9y + 18
6x + 18 = 5y + 15
- Simplify further:
11x - 9y = -4
6x - 5y = -3
- Multiply both sides of the second equation by 11 and the first equation by 6 to make the coefficients of x the same:
66x - 55y = -33
66x - 54y = -24
- Subtract the second equation from the first equation to eliminate x:
66x - 55y - (66x - 54y) = -33 - (-24)
-y = -9
y = 9
- Substitute the value of y back into one of the original equations (let's use the first one) to find the value of x:
(x + 2) / (9 + 2) = 9/11
(x + 2) / 11 = 9/11
11(x + 2) = 9(11)
11x + 22 = 99
11x = 77
x = 7
Therefore, the fraction is 7/9, which corresponds to option C.
Let's assume the original fraction is x/y.
According to the problem, when 2 is added to both the numerator and denominator, the fraction becomes 9/11. This can be represented by the equation:
(x + 2) / (y + 2) = 9/11
Similarly, when 3 is added to both the numerator and denominator, the fraction becomes 5/6. This can be represented by the equation:
(x + 3) / (y + 3) = 5/6
We now have a system of two equations with two variables. We can solve this system to find the values of x and y.
Solving the System of Equations:
- Multiply both sides of the first equation by (y + 2) and the second equation by (y + 3) to eliminate the denominators:
11(x + 2) = 9(y + 2)
6(x + 3) = 5(y + 3)
- Simplify and expand:
11x + 22 = 9y + 18
6x + 18 = 5y + 15
- Simplify further:
11x - 9y = -4
6x - 5y = -3
- Multiply both sides of the second equation by 11 and the first equation by 6 to make the coefficients of x the same:
66x - 55y = -33
66x - 54y = -24
- Subtract the second equation from the first equation to eliminate x:
66x - 55y - (66x - 54y) = -33 - (-24)
-y = -9
y = 9
- Substitute the value of y back into one of the original equations (let's use the first one) to find the value of x:
(x + 2) / (9 + 2) = 9/11
(x + 2) / 11 = 9/11
11(x + 2) = 9(11)
11x + 22 = 99
11x = 77
x = 7
Therefore, the fraction is 7/9, which corresponds to option C.
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A fraction becomes9/11, if 2 is added to both the numerator and denominator. If 3 is added to both the numerator and denominator it becomes5/6, then the fraction isa)9/7b)-9/7c)7/9d)-7/9Correct answer is option 'C'. Can you explain this answer?
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