if 1 is subtracted from numerator of a fraction the result is 3/4 and 6 is added to the denominator the result is 1/2. find the fraction by using substitution method
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if 1 is subtracted from numerator of a fraction the result is 3/4 and 6 is added to the denominator the result is 1/2. find the fraction by using substitution method
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Answer:
Step-by-step explanation:
Given that:
To Find:
Let us assume:
Where,
When 1 is subtracted from numerator of a fraction:
⇢ (x - 1)/y = 3/4
Cross multiplication.
⇢ 4(x - 1) = 3y
⇢ 4x - 4 = 3y ______(i)
When 6 is added to the denominator:
⇢ x/(y + 6) = 1/2
Cross multiplication.
⇢ 2x = y + 6
⇢ y = 2x - 6 ______(ii)
In equation (i).
⇢ 4x - 4 = 3y
Substituting the value of y from eqⁿ(ii).
⇢ 4x - 4 = 3(2x - 6)
⇢ 4x - 4 = 6x - 18
⇢ - 4 + 18 = 6x - 4x
⇢ 14 = 2x
⇢ x = 14/2
⇢ x = 7
Now in equation (ii).
⇢ y = 2x - 6
Substituting x.
⇢ y = (2 × 7) - 6
⇢ y = 14 - 6
⇢ y = 8
Therefore,
Answer:
Given :-
To Find :-
Method Used :-
Solution :-
Let, the numerator be x
And, the denominator will be y
Then,
[tex]\mapsto[/tex] [tex]\sf\bold{The\: fraction\: be\: =\: \dfrac{x}{y}}[/tex]
[tex]\leadsto[/tex] 1 is subtracted from the numerator of a fraction the result is 3/4 :
[tex]\implies \sf \dfrac{x - 1}{y} =\: \dfrac{3}{4}[/tex]
By doing cross multiplication we get,
[tex]\implies \sf 4(x - 1) =\: 3(y)[/tex]
[tex]\implies \sf 4x - 4 =\: 3y[/tex]
[tex]\implies \sf\bold{\purple{4x - 4 =\: 3y\: ------\: (Equation\: No\: 1)}}\\[/tex]
Again,
[tex]\leadsto[/tex] 6 is added to the denominator then the result is 1/2 :
[tex]\implies \sf \dfrac{x}{y + 6} =\: \dfrac{1}{2}[/tex]
By doing cross multiplication we get,
[tex]\implies \sf y + 6 =\: 2(x)[/tex]
[tex]\implies \sf y =\: 2x - 6[/tex]
[tex]\implies \sf\bold{\purple{y =\: 2x - 6\: ------\: (Equation\: No\: 2)}}\\[/tex]
Now, by putting the value of y in the equation no 1 we get,
[tex]\implies \sf 4x - 4 =\: 3y[/tex]
[tex]\implies \sf 4x - 4 =\: 3(2x - 6)[/tex]
[tex]\implies \sf 4x - 4 =\: 6x - 18[/tex]
[tex]\implies \sf 4x - 6x =\: - 18 + 4[/tex]
[tex]\implies \sf {\cancel{-}} 2x =\: {\cancel{-}} 14[/tex]
[tex]\implies \sf 2x =\: 14[/tex]
[tex]\implies\sf x =\: \dfrac{\cancel{14}}{\cancel{2}}[/tex]
[tex]\implies \sf\bold{\green{x =\: 7}}[/tex]
Again, by putting x = 7 in the equation no 1 we get,
[tex]\implies \sf 4x - 4 =\: 3y[/tex]
[tex]\implies \sf 4(7) - 4 =\: 3y[/tex]
[tex]\implies \sf 28 - 4 =\: 3y[/tex]
[tex]\implies \sf 24 =\: 3y[/tex]
[tex]\implies \sf \dfrac{\cancel{24}}{\cancel{3}} =\: y[/tex]
[tex]\implies \sf 8 =\: y[/tex]
[tex]\implies \sf\bold{\green{y =\: 8}}[/tex]
Hence, the required fraction will be :
[tex]\dashrightarrow \sf \dfrac{x}{y}[/tex]
[tex]\dashrightarrow \sf\bold{\red{\dfrac{7}{8}}}[/tex]
[tex]\therefore[/tex] The fraction is 7/8 .