Answer
To achieve the desired concentration of 30%, the chemist must add 400 mL of the 40% sucrose solution. Here’s how we figure it out: We need to calculate the total sucrose contribution for the final 30% concentration. Let x be the volume of the 40% solution added. The total volume becomes 200 + x mL and we set up the equation based on final concentration: 200 mL * 10% + x mL * 40% = (200 + x) mL * 30%. Converting percentages to decimals gives us 200 * 0.10 + x * 0.40 = (200 + x) * 0.30. Simplifying yields 20 + 0.4x = 60 + 0.3x. Rearranging gives 20 + 0.1x = 60. Subtracting 20 from both sides results in 0.1x = 40. Dividing by 0.1, we find x = 400 mL. Thus, 400 mL of the 40% solution is required.
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