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Question 1967: Plz help me in solving word problems involving linear equations in two variables.I want a full solution of my questions .
Q no:1) If 1 is subracted from the numerator and 2, added to the denominator of a fraction, it becomes 1/2. The fraction becomes 2/3, when 1 ,is subracted from its numerator and 2, from its denominator. 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 is formed is 54 less than the original number . Find the numbers.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! all "wordy" problems like this...start slowly. Read it a few times, see what they want you to find and define these things, so ...
Let original numerator = x
Let original denominator = y
so original fraction is x/y
(x-1)/(y+2) = 1/2 and also (x-1)/(y-2) = 2/3
That is the conversion of the English done. From now...purely maths
for each equation, get rid of the fractions:
2(x-1) = y+2 and 3(x-1) = 2(y-2)
2x-2 = y+2 and 3x-3 = 2y-4
2x-y = 4 and 3x-2y = -1
eqn1 is 2x-y = 4 --> scaled up to 4x-2y = 8 (just by multiplying every term by 2, so that the y term in both equation now matches.
eqn2 is 3x-2y = -1
4x-2y = 8
3x-2y = -1
Subtracting these together gives x = 9. Put this into either eqn1 or eqn2 gives y=14
so original fraction was 9/14.
AND NOW CHECK THAT THIS IS THE CORRECT ANSWER BY CHANGING IT AS STATED TO SEE IF YOU GET THE ANSWERS...
(9-1)/(14+2) --> 8/16 --> 1/2 : CORRECT!
(9-1)/(14-2) --> 8/12 --> 2/3 : CORRECT!
This is the beauty of maths...You now know you got this correct, so no worries. If these didn't work out, you know you did a mistake somewhere, so you can check and find it and correct it etc etc :-)
...Write an essay on the Russian Revolution 1910-1920...such an open-ended question. Maths is better :-)
cheers
Jon
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