SOLUTION: Plz help me in solving the linear equations involviing two variables.I want a full solution of my questions.My questions are: Q no:1= The sum of the numerator and the denominato

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Question 1792: Plz help me in solving the linear equations involviing two variables.I want a full solution of my questions.My questions are:
Q no:1= The sum of the numerator and the denominator of a fraction is 10. If the numerator is multiplied by 3 and the denominator by 1/2, the fraction becomes 2/3. Find the fraction.?
Q no:2= A number consists of two digits . THe digit at ten's place is 4 times the digit at unit's place. On changing the place of digits , the new number formed is 54 less than the original number. Find the number?

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
Q1... let the fraction be a/b.
we know a + b = 10 ...equation 1.
We also know that %283a%29%2F%28b%2F2%29+=+2%2F3
this is %286a%2Fb%29+=+2%2F3
substitute in for b from equation 1, gives
%286a%2F%2810-a%29%29+=+2%2F3
cross-multiply to give 18a+=+2%2810-a%29 which becomes 18a+=+%2820-2a%29. Re-arranging this gives 20a = 20, therefore a=1. Solve for b, gives b=9.

Q2...this you can do by just looking...the tens digit is 4 times the unit digit...the only numbers that have this are 2 and 8....you have 28 and 82, a difference of 54. Done.
cheers
Jon.