b) How many liters of \( 10 \% \) saline solution must be added to \( 18 \% \) saline solution to make 5 liters \( 13 \% \) saline solution?

To solve this problem, we can use the concept of mixing solutions. Let's denote the amount of \( 10\% \) saline solution to be added as \( x \) liters. The amount of salt in the \( 10\% \) saline solution is \( 0.10x \) liters. The amount of salt in the \( 18\% \) saline solution is \( 0.18(5-x) \) liters. The total amount of salt in the final solution is \( 0.13 \times 5 \) liters. We can set up an equation based on the total amount of salt in the final solution: \[ 0.10x + 0.18(5-x) = 0.13 \times 5 \] Now, we can solve this equation to find the value of \( x \), which represents the amount of \( 10\% \) saline solution to be added. Solve the equation by following steps: - step0: Solve for \(x\): \(0.1x+0.18\left(5-x\right)=0.13\times 5\) - step1: Multiply the numbers: \(0.1x+0.18\left(5-x\right)=0.65\) - step2: Move the expression to the left side: \(0.1x+0.18\left(5-x\right)-0.65=0\) - step3: Calculate: \(-0.08x+0.25=0\) - step4: Move the constant to the right side: \(-0.08x=0-0.25\) - step5: Remove 0: \(-0.08x=-0.25\) - step6: Change the signs: \(0.08x=0.25\) - step7: Divide both sides: \(\frac{0.08x}{0.08}=\frac{0.25}{0.08}\) - step8: Divide the numbers: \(x=\frac{25}{8}\) The amount of \( 10\% \) saline solution that must be added to \( 18\% \) saline solution to make 5 liters of \( 13\% \) saline solution is \( 3.125 \) liters.