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. $150\operatorname{\mathrm{m}\mathrm{L}}$
• D. $250\operatorname{\mathrm{m}\mathrm{L}}$

Answer: (C)

Verified step by step guidance

1. Identify the known quantities: the initial volume of syrup is 300 mL with 45% sugar concentration, and the desired concentration after dilution is 30%. Let the volume of water to add be \( x \) mL.
2. Express the amount of sugar before dilution: since the syrup is 45% sugar, the sugar amount is \( 0.45 \times 300 \) mL.
3. After adding \( x \) mL of water, the total volume becomes \( 300 + x \) mL, but the amount of sugar remains the same because water contains no sugar.
4. Set up the equation for the final concentration: the sugar amount divided by the new total volume equals 30%, so \( \frac{0.45 \times 300}{300 + x} = 0.30 \).
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.