For Items \( \mathbf{1 6 - 2 0} \), solve each equation and chec your solutions. 16. \( 6 x=36 \) 17. \( 350=140 r \) 19. \( 7.8 s=499.2 \) 20. \( \frac{1}{5} k=15 \) 21. \( \frac{5}{6} x=\frac{25}{36} \) 22. \( \frac{4}{9} x=\frac{8}{27} \)

Solve the equation by following steps: - step0: Solve for \(k\): \(\frac{1}{5}k=15\) - step1: Multiply by the reciprocal: \(\frac{1}{5}k\times 5=15\times 5\) - step2: Multiply: \(k=75\) Solve the equation \( \frac{4}{9}x=\frac{8}{27} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{4}{9}x=\frac{8}{27}\) - step1: Multiply by the reciprocal: \(\frac{4}{9}x\times \frac{9}{4}=\frac{8}{27}\times \frac{9}{4}\) - step2: Multiply: \(x=\frac{2}{3}\) Solve the equation \( 7.8s=499.2 \). Solve the equation by following steps: - step0: Solve for \(s\): \(7.8s=499.2\) - step1: Divide both sides: \(\frac{7.8s}{7.8}=\frac{499.2}{7.8}\) - step2: Divide the numbers: \(s=64\) Solve the equation \( \frac{5}{6}x=\frac{25}{36} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{5}{6}x=\frac{25}{36}\) - step1: Multiply by the reciprocal: \(\frac{5}{6}x\times \frac{6}{5}=\frac{25}{36}\times \frac{6}{5}\) - step2: Multiply: \(x=\frac{5}{6}\) Solve the equation \( 6x=36 \). Solve the equation by following steps: - step0: Solve for \(x\): \(6x=36\) - step1: Divide both sides: \(\frac{6x}{6}=\frac{36}{6}\) - step2: Divide the numbers: \(x=6\) Solve the equation \( 350=140r \). Solve the equation by following steps: - step0: Solve for \(r\): \(350=140r\) - step1: Swap the sides: \(140r=350\) - step2: Divide both sides: \(\frac{140r}{140}=\frac{350}{140}\) - step3: Divide the numbers: \(r=\frac{5}{2}\) Let's solve each equation step by step and check the solutions. ### 16. Solve \( 6x = 36 \) To solve for \( x \): \[ x = \frac{36}{6} = 6 \] **Check:** \[ 6 \cdot 6 = 36 \quad \text{(True)} \] ### 17. Solve \( 350 = 140r \) To solve for \( r \): \[ r = \frac{350}{140} = \frac{5}{2} = 2.5 \] **Check:** \[ 140 \cdot 2.5 = 350 \quad \text{(True)} \] ### 19. Solve \( 7.8s = 499.2 \) To solve for \( s \): \[ s = \frac{499.2}{7.8} = 64 \] **Check:** \[ 7.8 \cdot 64 = 499.2 \quad \text{(True)} \] ### 20. Solve \( \frac{1}{5}k = 15 \) To solve for \( k \): \[ k = 15 \cdot 5 = 75 \] **Check:** \[ \frac{1}{5} \cdot 75 = 15 \quad \text{(True)} \] ### 21. Solve \( \frac{5}{6}x = \frac{25}{36} \) To solve for \( x \): \[ x = \frac{25}{36} \cdot \frac{6}{5} = \frac{5}{6} \] **Check:** \[ \frac{5}{6} \cdot \frac{5}{6} = \frac{25}{36} \quad \text{(True)} \] ### 22. Solve \( \frac{4}{9}x = \frac{8}{27} \) To solve for \( x \): \[ x = \frac{8}{27} \cdot \frac{9}{4} = \frac{2}{3} \] **Check:** \[ \frac{4}{9} \cdot \frac{2}{3} = \frac{8}{27} \quad \text{(True)} \] ### Summary of Solutions: - \( x = 6 \) - \( r = 2.5 \) - \( s = 64 \) - \( k = 75 \) - \( x = \frac{5}{6} \) - \( x = \frac{2}{3} \)