6. The area of a rectangle is 14 square units. It has side lengths \( x \) and \( y \). Given each value for \( x \), find \( y \). a, \( x=2 \frac{1}{3} \) b. \( x=4 \frac{1}{5} \) c. \( x=\frac{7}{6} \) c. \( 125 \% \) (From Unit 3 , Lesson 11. ) b. \( 75 \% \) (From Unit 4 , Lesson 13 .) 7. Lin needs to save up \( \$ 20 \) for a new game. How much money does she have if she has saved each percentage of her goal. Explain your reasoning. a. \( 25 \% \)

Let's solve the problems step by step. ### Problem 6: Finding \( y \) given \( x \) The area \( A \) of a rectangle is given by the formula: \[ A = x \cdot y \] Given that the area is 14 square units, we can express \( y \) in terms of \( x \): \[ y = \frac{A}{x} = \frac{14}{x} \] Now, we will calculate \( y \) for each given value of \( x \). #### a. \( x = 2 \frac{1}{3} \) First, convert \( x \) to an improper fraction: \[ x = 2 \frac{1}{3} = \frac{7}{3} \] Now, substitute \( x \) into the equation for \( y \): \[ y = \frac{14}{\frac{7}{3}} = 14 \cdot \frac{3}{7} = 6 \] #### b. \( x = 4 \frac{1}{5} \) Convert \( x \) to an improper fraction: \[ x = 4 \frac{1}{5} = \frac{21}{5} \] Now, substitute \( x \) into the equation for \( y \): \[ y = \frac{14}{\frac{21}{5}} = 14 \cdot \frac{5}{21} = \frac{70}{21} = \frac{10}{3} \approx 3.33 \] #### c. \( x = \frac{7}{6} \) Substitute \( x \) into the equation for \( y \): \[ y = \frac{14}{\frac{7}{6}} = 14 \cdot \frac{6}{7} = 12 \] #### d. \( x = 125\% \) Convert \( 125\% \) to a decimal: \[ x = 1.25 \] Now, substitute \( x \) into the equation for \( y \): \[ y = \frac{14}{1.25} = 11.2 \] #### e. \( x = 75\% \) Convert \( 75\% \) to a decimal: \[ x = 0.75 \] Now, substitute \( x \) into the equation for \( y \): \[ y = \frac{14}{0.75} = \frac{14 \cdot 100}{75} = \frac{1400}{75} = \frac{280}{15} \approx 18.67 \] ### Summary of Results for Problem 6: - a. \( y = 6 \) - b. \( y = \frac{10}{3} \) or approximately \( 3.33 \) - c. \( y = 12 \) - d. \( y = 11.2 \) - e. \( y \approx 18.67 \) --- ### Problem 7: Lin's Savings Lin needs to save \( \$20 \) for a new game. We need to find out how much money she has saved for each percentage of her goal. The amount saved can be calculated using the formula: \[ \text{Amount Saved} = \text{Percentage} \times \text{Total Goal} \] #### a. \( 25\% \) Convert \( 25\% \) to a decimal: \[ \text{Percentage} = 0.25 \] Now, calculate the amount saved: \[ \text{Amount Saved} = 0.25 \times 20 = 5 \] ### Summary of Results for Problem 7: - a. Lin has saved \( \$5 \) if she has saved \( 25\% \) of her goal. This concludes the solutions for both problems. If you have any further questions or need additional calculations, feel free to ask!