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# Word Problems/Math

Question
1)Danny invested some money at 3% simple interest and some money at 7% simple interest. The amount invested at the higher rate was \$3000 more than the amount invested at the lower rate. If the total interest on the investments for one year was \$810, then how much did he invest at each rate?

2)how many liters of a 10% alcohol solution should be mixed with 12 liters of a 20% alcohol solution to obtain a 14% alcohol solution?

")Danny invested some money at 3% simple interest and some money at 7% simple interest."
x = amount invested at 3%
y = amount invested at 7%

"The amount invested at the higher rate was \$3000 more than the amount invested at the lower rate."
y = x + 3000

"the total interest on the investments for one year was \$810"
0.03x + 0.07y = 810

substitution
0.03x + 0.07(x + 3000) = 810
x = 6000
y = x + 3000 = 9000
:::::
"how many liters of a 10% alcohol solution should be mixed with 12 liters of a 20% alcohol solution to obtain a 14% alcohol solution?"
x liters of 10% solution contain 0.10x liters of alcohol
12 liters of 20% solution contain 0.20·12 = 2.4 liters of alcohol

total volume = 12 + x liters
12 + x liters of 14% solution contain 0.14(12 + x) = 1.68 + 0.14x liters of alcohol

1.68 + 0.14x = 0.10x + 2.4
x = 18

18 liters of 10% solution mixed with 12 liters of 20% solution yields 30 liters of 14% solution.

Word Problems

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#### Janet Yang

##### Expertise

Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

##### Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.