Answer to Question #136524 in Algebra for Faith

Question

1. Use a proportion to solve each problem.
1.1. the numerator of a certain fraction is 3 times the denominator.if the numerator is decreased by 1 and the denominator is increased by 2,the value of the resulting fraction is 5/2.find the original fraction.
1.2. thenjo can wash 6 chairs in 21 minutes.how many minutes would it take thenjo to wash 10 chairs?

Answer 1

$(1)\\ \displaystyle\textsf{Let the fraction be}\hspace{0.1cm} \frac{x}{y}\\ \frac{x}{y} = \frac{3y}{y}\\ \displaystyle\frac{3y - 1}{y + 2} = \frac{5}{2}\\ \begin{aligned} 2(3y - 1) &= 5(y + 2)\\ 6y - 2 &= 5y + 10\\ y &=10 + 2 = 12 \end{aligned}\\ \therefore \textsf{The original fraction is}\hspace{0.1cm} \frac{x}{y} = \frac{36}{12}.\\ (2)\\ 6\hspace{0.1cm} \textsf{chairs can be washed in} \hspace{0.1cm}21\hspace{0.1cm} \textsf{minutes}. \\ 1\hspace{0.1cm} \textsf{chair can be washed in} \hspace{0.1cm}\frac{21}{6}\hspace{0.1cm} \textsf{minutes}. \\ \therefore 10\hspace{0.1cm} \textsf{chairs can be washed in} \\\hspace{0.1cm}\frac{21\times 10}{6}= 35\hspace{0.1cm} \textsf{minutes}.$