Santa tasted 500 ml of a 60% solution of eggnog. How many milliliters of a 30% eggnog solution should be added to obtain a 50% solution?
.3n + .5(500+ n)=300 n = 62.5ml
.3n +.5(500 + n) =300
.3n + 250 + .5n = 300
.8n + 250 =300
.8n = 50
500*.6 + V*.3= .5(500+V)
solve for V
To solve this problem, we need to use the concept of mixing solutions of different concentrations to obtain a desired concentration. Here's how we can proceed:
Let's assume that x milliliters of the 30% eggnog solution needs to be added.
1. We'll start by calculating the amount of eggnog in the 60% solution.
- The amount of eggnog in the 60% solution is 60% of 500 ml, which is (60/100) * 500 = 300 ml.
2. Next, we can calculate the amount of eggnog in the 30% solution that needs to be added.
- The amount of eggnog in the 30% solution is 30% of x ml, which is (30/100) * x = 0.3x ml.
3. Now, we can set up an equation based on the total amount of eggnog in the final mixture.
- The total amount of eggnog in the final mixture should be the sum of eggnog in the initial 60% solution and the additional 30% solution. So we have: 300 ml + 0.3x ml = 0.5 * (500 ml + x ml).
4. Solving the equation:
- Distribute 0.5 on the right side of the equation: 300 ml + 0.3x ml = 250 ml + 0.5x ml.
- Rearrange the equation: 0.3x ml - 0.5x ml = 250 ml - 300 ml.
- Combine like terms: -0.2x ml = -50 ml.
- Divide both sides by -0.2: x ml = (-50 ml) / (-0.2).
- Simplify: x ml = 250 ml.
Therefore, 250 ml of the 30% eggnog solution should be added to the 500 ml of the 60% eggnog solution to obtain a 50% eggnog solution.