5 is wrong. The answer should be 7. Solve 1 + 0.8y = 0.6(4 + y) for y and get 7.
I agree with the rest of your answers.
I have collected few interesting mixture problems. I do not know the original answers to these but I solved them using my technique and would like to verify my answers with yours. I am including my answers in spoilers so that you don't see it right away
1. Mixture A is 15 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
SPOILER: 2.3
2. A chemist needs to mix a 10 % acid solution with 35% acid solution to end up with 1000 milliters of a 25% acid solution. How much of each solution is needed?
SPOILER: 400, 600
3. If 3 liters of 40% orange juice and 1 liter of 50% orange juice are mixed which of the following is the percentage of orange juice in the mixture?
SPOILER: 42.5%
4. One liquid solution of 7 liters contains 40 % water. A second liquid solution of 18 liters contain 20% water. If these two solutions are mixed, what percent of the mixture is water?
SPOILER: 25.6%
5. Dr. Tik needs to make a solution that is 60% alcohol. if she has 4 liters of a solution that is 25% alcohol, how many of 80% solution will she need to add?
SPOILER: 2.5 lit
6. A mixture of 12 ounces of vinegar and oil is 40%n vinegar by weight. How many ounces of oil must be added to the mixtue to produce a new mixture that is only 25% vinegar?
SPOILER: 7.2 ounce
7. Two solutions of 90% and 97% purity are mixed resulting in 21liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
SPOILER: 9 litres
8. A mixture of 20ltrs of brandy and water contains 10% water. How much water should be added to it to increase the percentage of water to 25%?
SPOILER: 4 litrs
9. A cistern contains 50 liters of water. 5 litres of water is taken out of it adn replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
SPOILER: 19/81
1. Solve 0.15A + 0.5B = 1.2 and A + B = 4. We have 1.2 on the right side of the first equation because you need to get a 4 gallon mixture of 30% alcohol and 0.3*4 = 1.2.
2. Same idea, solve 0.1A + 0.35B = 250 and A + B = 1000.
3. You have 0.4*3 + 0.5*1 = 1.7 liters of orange juice in a 4 liter mixture, so 1.7/4 = 0.425.
4. Same idea as 3, you have 0.4*7 + 0.2*18 = 6.4 liters of water in a 25 liter mixture, so 6.4/25 = 0.256.
5. Solve 0.6(4+y) = 1 + 0.8y for y and get y = 7.
I'll do the rest later, have to go to a meeting.
Please post only one question per thread. Otherwise things can become pretty complicated when there are discussions on multiple questions.
Cheers,
Brent
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