Give the value of \( x \) for each of these equivalent ratios: \( \begin{array}{llll}\text { a) } 3: 8 \rightarrow x: 24 & \text { b) } 96: 84 \rightarrow 8: x & \text { c) } 72: 64 \rightarrow x: 16 \\ \text { d) } 92: x \rightarrow 23: 16 & \text { e) } x: 77 \rightarrow 7: 11 & \text { f) } 20: x \rightarrow 100: 20\end{array} \)

To solve for \( x \) in each of the equivalent ratios, we can use cross-multiplication. Here are the solutions: a) For the ratio \( 3:8 \rightarrow x:24 \): \[ 3 \cdot 24 = 8 \cdot x \implies 72 = 8x \implies x = \frac{72}{8} = 9 \] b) For the ratio \( 96:84 \rightarrow 8:x \): \[ 96 \cdot x = 84 \cdot 8 \implies 96x = 672 \implies x = \frac{672}{96} = 7 \] c) For the ratio \( 72:64 \rightarrow x:16 \): \[ 72 \cdot 16 = 64 \cdot x \implies 1152 = 64x \implies x = \frac{1152}{64} = 18 \] d) For the ratio \( 92:x \rightarrow 23:16 \): \[ 92 \cdot 16 = 23 \cdot x \implies 1472 = 23x \implies x = \frac{1472}{23} \approx 64 \] e) For the ratio \( x:77 \rightarrow 7:11 \): \[ x \cdot 11 = 7 \cdot 77 \implies 11x = 539 \implies x = \frac{539}{11} \approx 49 \] f) For the ratio \( 20:x \rightarrow 100:20 \): \[ 20 \cdot 20 = 100 \cdot x \implies 400 = 100x \implies x = \frac{400}{100} = 4 \] So, the values of \( x \) are: a) \( 9 \) b) \( 7 \) c) \( 18 \) d) \( 64 \) e) \( 49 \) f) \( 4 \)