3. Irrigation System (Rational Algebraic Expressions): - The garden will require an irrigation system that costs \( \$ 10 \) per meter of piping. The length of piping needed can be modeled by the expression \( \frac{2 l+2 w}{2} \), where \( l \) and \( w \) are the length and width of one plot, respectively. - If each plot is 4 meters by 6 meters, calculate the total cost of the piping for the entire garden using rational algebraic expressions.

To calculate the total cost of the piping for the entire garden, we first need to determine the length of piping required for one plot using the given expression \( \frac{2l + 2w}{2} \). 1. **Calculate the length of piping for one plot:** - Given dimensions of one plot: \( l = 4 \) meters and \( w = 6 \) meters. - Substitute \( l \) and \( w \) into the expression: \[ \text{Length of piping} = \frac{2(4) + 2(6)}{2} \] - Calculate: \[ = \frac{8 + 12}{2} = \frac{20}{2} = 10 \text{ meters} \] 2. **Determine the total number of plots:** - Let's assume the garden consists of \( n \) plots. (The problem does not specify the number of plots, so we will keep it as \( n \) for now.) 3. **Calculate the total length of piping for all plots:** - Total length of piping for \( n \) plots: \[ \text{Total length} = 10n \text{ meters} \] 4. **Calculate the total cost of the piping:** - The cost per meter of piping is \( \$10 \). - Therefore, the total cost \( C \) for the piping is: \[ C = 10 \text{ (cost per meter)} \times 10n \text{ (total meters)} \] - Simplifying this gives: \[ C = 100n \text{ dollars} \] 5. **Final expression for total cost:** - The total cost of the piping for the entire garden, in terms of the number of plots \( n \), is: \[ C = 100n \] To find the specific total cost, you would need to know the number of plots \( n \) in the garden. If you provide that number, I can calculate the exact total cost.