A fraction's value is 4/5. When its numerator
is increased by 9, the new fraction equals
the reciprocal of the value of the original
fraction. Find the original fraction.
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A fraction's value is 4/5. When its numerator
is increased by 9, the new fraction equals
the reciprocal of the value of the original
fraction. Find the original fraction.
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Verified answer
Let :
Given :
[tex]\sf \bullet \: \: \dfrac{x}{y} = \dfrac{4}{5} [/tex]
[tex]\sf \bullet \: \: \dfrac{x + 3}{y} = \dfrac{y}{x} = \dfrac{5}{4} [/tex]
To find :
[tex] \sf \: \dfrac{x}{y} [/tex]
Solution :
[tex]\sf \: \: x = \dfrac{4y}{5} \: \: .......equation1 [/tex]
[tex]\sf \implies \: \: \: \dfrac{x + 9}{y} = \dfrac{5}{4} \\ \\ \sf \implies \: \: x + 9= \dfrac{5}{4} y \\ \\ \sf \: putting \: value \: of \: x \: from \: equation \: 1 \: we \: get \: \\ \sf \implies \: ( \dfrac{4y}{5} ) + 9= \dfrac{5y}{4} \\ \\ \sf \implies \: 0.8y + 9 = 1.25y \\ \sf \implies \: 1.25y - 0.8y = 9 \\ \sf \implies \: 0.45y = 9 \\ \sf \implies \: y \: = \: \dfrac{9}{0.45} = 20[/tex]
Putting value of y in equation 1, we get;
x = 4×20/5 = 4×4
x = 16
ANSWER :
Numerator (x) = 16
Denominator (y) = 20
[tex] \sf \bold{Fraction = \dfrac{16}{20} }[/tex]