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Word Problems/math fraction problem

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Question
QUESTION: A jar 1/6 filled with beads has a mass of 2 1/2 kg. When it is completely filled with beads, it has a mass of 6 1/2 kg. What is the mass of the empty jar?

ANSWER: "A jar 1/6 filled with beads has a mass of 2 1/2 kg. When it is completely filled with beads, it has a mass of 6 1/2 kg."
jar + beads = 6.5 kg
jar + (1/6)beads = 2.5 kg

subtract the second equation from the first:
(5/6) beads = 4 kg

beads = 46/5 = 4.8 kg

jar = 6.5 kg - 4.8 kg = 1.7 kg


---------- FOLLOW-UP ----------

QUESTION: "James gave 1/4 of his money to his mother. He spent 5/18 of the remainder on a wallet and 2 CDs and had $78 left. The wallet cost 4 times as much as a CD.
(a) How much money did James have at first?
(b) What was the cost of one CD?"

Answer
x = starting amount of money

"James gave 1/4 of his money to his mother."
He had (3/4)x remaining.

"He spent 5/18 of the remainder on a wallet and 2 CDs and had $78 left."
(13/18)(3/4)x = $78
x = $144
James started out with $144.
:::::
The wallet and 2CDs cost (5/18)(3/4)x = $30.

"The wallet cost 4 times as much as a CD."
The wallet and 2CDs cost as much as 6 CDs.
One CD cost $30/6 = $5.

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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.

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

Education/Credentials
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.

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

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