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Julli [10]
4 years ago
11

 The denominator of a fraction in simplest form is greater than the numerator by 3. If 7 is added to the numerator, and 5 added

to the denominator, then the fraction itself is increased by 1/2 . Find the original fraction.
Mathematics
1 answer:
jok3333 [9.3K]4 years ago
4 0
So.. if we take the numerator to be say "a", then the denominator will be "a+3"

\bf \cfrac{a}{a+3}\textit{ if we add }\frac{1}{2}\textit{ we get then }\cfrac{a+7}{a+3+5}
\\\\\\
thus\implies \cfrac{a}{a+3}+\cfrac{1}{2}=\cfrac{a+7}{a+8}\\\\
-----------------------------\\\\
\cfrac{a+3+2a}{2(a+3)}=\cfrac{a+7}{a+8}\implies \cfrac{3a+3}{2a+6}=\cfrac{a+7}{a+8}
\\\\\\
3a^2+24a+3a+24=2a^2+14a+6a+42
\\\\\\
a^2+7a-18=0\implies (a+9)(a-2)=0
\\\\\\
a=
\begin{cases}
2\implies &\frac{2}{5}\\\\
-9\implies &\frac{3}{2}
\end{cases}

either of those two fractions will do
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Given:

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Therefore, the required system of inequalities contains some equations,  x+y\leq 13,4x+7y\geq 65 and x, y\geq 0.

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Answer:

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