Question

Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?

Accepted Answer

Identify the known quantities: the initial volume of the saline solution is 8 mL, and its concentration is 6%. The final concentration after adding water should be 4%. Let the volume of water to be added be $$ x  mL. $$Set up the equation based on the fact that the amount of salt (solute) remains constant before and after dilution. The amount of salt initially is $$ 8 	imes 0.06 . $$After adding water, the total volume is $$ 8 + x  mL$$, and the concentration is 4%, so the amount of salt is $$ (8 + x) 	imes 0.04 . $$Write the equation representing the conservation of salt: $$ 8 	imes 0.06 = (8 + x) 	imes 0.04 . $$Solve the equation for $$ x  by $$first expanding the right side: $$ 0.48 = 0.04 	imes 8 + 0.04x $$, then isolate $$ x  by $$subtracting $$ 0.32 $$ from both sides and dividing by $$ 0.04 . $$Interpret the solution for $$ x  as $$the volume of water in milliliters that must be added to reduce the saline concentration from 6% to 4%.

Solve each problem. See Example 3. How much water should be added to 8 mL of 6% saline solution to reduce the concentration to 4%?

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Key Concepts

Concentration and Percentage Solutions

Dilution Principle

Setting Up and Solving Equations