A 25-ounce solution is $20 \%$ alcohol. If 50 ounces of water are added to it, what percent of the new solution is alcohol?
(A) $6 \frac{2}{3} \%$
(B) $7 \frac{1}{2} \%$
(C) $10 \%$
(D) $13 \frac{1}{3} \%$
Answer (2)
The percentage of alcohol in the new solution after adding 50 ounces of water is approximately 6 3 2 % . This is derived from calculating the initial amount of alcohol and dividing it by the new total volume of the solution. Therefore, the correct answer is (A).
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Calculate the amount of alcohol in the initial solution: 25 × 0.20 = 5 ounces.
Calculate the total volume of the new solution: 25 + 50 = 75 ounces.
Calculate the percentage of alcohol in the new solution: 75 5 × 100 = 6 3 2 % .
The percentage of alcohol in the new solution is 6 3 2 % .
Explanation
Problem Analysis We are given a 25-ounce solution that is 20% alcohol. We need to find the percentage of alcohol in the new solution after adding 50 ounces of water.
Calculate Amount of Alcohol First, calculate the amount of alcohol in the initial solution. This is done by multiplying the total volume of the initial solution by the percentage of alcohol: A l co h o l = 25 ounces × 20% = 25 × 0.20 = 5 ounces So, there are 5 ounces of alcohol in the initial solution.
Calculate New Volume Next, calculate the total volume of the new solution after adding 50 ounces of water: N e w V o l u m e = I ni t ia l V o l u m e + Wa t er A dd e d = 25 + 50 = 75 ounces The new solution has a total volume of 75 ounces.
Calculate New Percentage Now, calculate the percentage of alcohol in the new solution by dividing the amount of alcohol by the new volume and multiplying by 100: P erce n t a g e = N e w V o l u m e A l co h o l × 100 = 75 5 × 100 = 15 1 × 100 = 6.666...% Rounding to one decimal place, the percentage of alcohol in the new solution is approximately 6.67%.
Final Answer The percentage of alcohol in the new solution is 6.666...% , which is equal to 6 3 2 % . Therefore, the correct answer is (A).
Examples
Imagine you're mixing a fruit punch for a party. You start with a mix that's 20% juice concentrate, but it's too strong. By adding water, you dilute the concentrate. This problem helps you calculate the new concentration of juice in the punch, ensuring it's just right for your guests. Understanding how to calculate percentages in mixtures is useful in many real-life situations, from cooking to chemistry.
