A candy maker has $300\mathrm{mL}$ of a $45\%$ sugar syrup. She wants to dilute it with pure water to make a $30\%$ syrup. How many $mL$ of water should she add?

• A. $450\mathrm{mL}$
• B. $750\mathrm{mL}$
• C. $150\mathrm{mL}$
• D. $250\mathrm{mL}$

Answer: (C)

Verified step by step guidance

1. Identify the amount of sugar in the original syrup by multiplying the volume of the syrup by its sugar concentration: calculate \(300 \operatorname{mL} \times 0.45\) to find the sugar content in milliliters.
2. Let \(x\) represent the amount of pure water (0% sugar) to be added. The total volume after adding water will be \$300 + x$ milliliters.
3. Set up an equation for the final concentration of sugar after dilution. The amount of sugar remains the same, but the total volume changes, so the concentration is \(\frac{\text{sugar amount}}{300 + x} = 0.30\).
4. Substitute the sugar amount from step 1 into the equation: \(\frac{300 \times 0.45}{300 + x} = 0.30\).
5. Solve the equation for \(x\) by multiplying both sides by \((300 + x)\), then isolating \(x\) on one side to find the volume of water to add.