AMC 10 2020a

What value of $x$ satisfies $$x- \frac{3}{4} = \frac{5}{12} - \frac{1}{3}?$$ $\textbf{(A)}\ -\frac{2}{3} \textbf{(B)}\ \frac{7}{36} \textbf{(C)}\ \frac{7}{12} \textbf{(D)}\ \frac{2}{3} \textbf{(E)}\ \frac{5}{6}$

The numbers $3, 5, 7, a,$ and $b$ have an average (arithmetic mean) of $15$ . What is the average of $a$ and $b$ ? $\textbf{(A) } 0 \textbf{(B) } 15 \textbf{(C) } 30 \textbf{(D) } 45 \textbf{(E) } 60$

Assuming $a\neq3$ , $b\neq4$ , and $c\neq5$ , what is the value in simplest form of the following expression? $$\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}$$ $\textbf{(A) } -1 \textbf{(B) } 1 \textbf{(C) } \frac{abc}{60} \textbf{(D) } \frac{1}{abc} - \frac{1}{60} \textbf{(E) } \frac{1}{60} - \frac{1}{abc}$