SOLUTION: A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the
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-> SOLUTION: A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the
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Question 557615: A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the resulting fraction is the recipricol of the original fraction. Find the original fraction.
Thanks!(: Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website! A fraction has a value of 4/7. The two digits in the numerator are interchanged in the denominator. If 11 is added to the numerator, and 22 is subtracted from the denominator, the resulting fraction is the recipricol of the original fraction. Find the original fraction.
tens digit of the numerator = t
units digit of the numerator = u
Numerator = 10t + u
>>...The two digits in the numerator are interchanged in the denominator...<<
tens digit of the denominator = u
units digit of the denominator = t
denominator = 10u + t
>>...A fraction has a value of ...<<
=
>>...If 11 is added to the numerator, and 22 is subtracted from the
denominator, the resulting fraction is the recipricol of the
original fraction...<<
=
So we have this system of equations to solve:
We simplify the first equation:
=
Cross-multiply:
7(10t + u) = 4(10u + t)
70t + 7u = 40u + 4t
66t = 33u
Divide both sides by 33
2t = u
Cross-multiply:
4(10t + u + 11) = 7(10u + t - 22)
40t + 4u + 44 = 70u + 7t - 154
33t + 198 = 66u
Divide both sides by 33
t + 6 = 2u
So the system is now
Solve that by substitution and get
t = 2, u = 4
numerator = 10t + u = 10(2) + 4 = 20 + 4 = 24
denominator = 10u + t = 10(4) + 2 = 40 + 2 = 42
fraction =
Edwin