Question

Question 1(Multiple Choice Worth 5 points)

(07.10A)

If 4 over 5 ton of concrete covers 5 over 6 of a bridge, how many tons of concrete are required to cover the entire bridge?

1 over 5 ton
9 over 30 ton
2 over 3 ton
24 over 25 ton

Answer 1

well, to cover the whole bridge, is 6/6, or 1 whole

so hmmm   $\bf \begin{array}{ccllll} concrete&bridge\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ \frac{4}{5}&\frac{5}{6}\\\\ x&\frac{6}{6} \end{array}\implies \cfrac{\frac{4}{5}}{x}=\cfrac{\frac{5}{6}}{\frac{6}{6}}\implies \cfrac{\frac{4}{5}}{\frac{x}{1}}=\cfrac{\frac{5}{6}}{\frac{6}{6}}$

$\bf \cfrac{4}{5}\cdot \cfrac{1}{x}=\cfrac{5}{6}\cdot \cfrac{6}{6}\implies \cfrac{4}{5x}=\cfrac{5}{6}\implies 4\cdot 6=5\cdot 5x\implies 24=25x \\\\\\ \boxed{\cfrac{24}{25}}=x$