Question

Fraction a/b is equivalent to 7/20, and a + b = 135. Find fraction a/b.

Answer 1

$\begin{cases} \frac{a}{b}=\frac{7}{20}\\a+b=135\end{cases}\\ \\b\neq 0 \\ \\\begin{cases} \frac{a}{b}=\frac{7}{20} \\a =135 - b\end{cases}\\ \\\begin{cases} \frac{135 - b}{b}=\frac{7}{20} \\a =135 - b\end{cases}$

$\begin{cases} 20(135 - b) = 7b \\a =135 - b\end{cases}\\ \\ \begin{cases} 2700- 20b = 7b \\a =135 - b\end{cases}\\ \\ \begin{cases} 2700 = 7b+20b \\a =135 - b\end{cases}\\ \\\begin{cases} 27b =2700 \ \ /:27 \\a =135 - b\end{cases}$

$\begin{cases} b = 100 \\a =135 - 100\end{cases}\\ \\ \begin{cases} b = 100 \\a = 35 \end{cases} \\ \\ \frac{a}{b}=\frac{7}{20}\\ \\ \frac{\not35^7 }{\not100^{20} }=\frac{7}{20}\\ \\ \frac{7}{20}=\frac{7}{20} \\ \\L=P$