a) How many liters of \( 16 \% \) weed killer mixture must be added to 3 liters of \( 5 \% \) weed killer mixture to make a \( 10 \% \) weed killer mixture?

To solve this problem, we can set up an equation based on the concentration of the weed killer mixtures. Let \( x \) be the number of liters of the \( 16\% \) weed killer mixture that we need to add. 1. **Calculate the amount of active ingredient in each mixture:** - The \( 5\% \) mixture has \( 3 \) liters, so the amount of active ingredient in it is: \[ 0.05 \times 3 = 0.15 \text{ liters} \] - The \( 16\% \) mixture has \( x \) liters, so the amount of active ingredient in it is: \[ 0.16 \times x = 0.16x \text{ liters} \] 2. **Total volume of the new mixture:** - The total volume of the new mixture will be \( 3 + x \) liters. 3. **Total amount of active ingredient in the new mixture:** - The total amount of active ingredient in the new mixture will be: \[ 0.15 + 0.16x \text{ liters} \] 4. **Set up the equation for the desired concentration:** - We want the new mixture to be \( 10\% \). Therefore, we can set up the equation: \[ \frac{0.15 + 0.16x}{3 + x} = 0.10 \] 5. **Solve the equation:** - Cross-multiply to eliminate the fraction: \[ 0.15 + 0.16x = 0.10(3 + x) \] - Distributing the \( 0.10 \): \[ 0.15 + 0.16x = 0.30 + 0.10x \] - Rearranging the equation: \[ 0.16x - 0.10x = 0.30 - 0.15 \] \[ 0.06x = 0.15 \] - Solving for \( x \): \[ x = \frac{0.15}{0.06} = 2.5 \] Thus, you need to add **2.5 liters** of the \( 16\% \) weed killer mixture to the \( 3 \) liters of the \( 5\% \) weed killer mixture to obtain a \( 10\% \) weed killer mixture.