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April 25th, 2017, 11:01 PM   #1
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Rational Expression Questions

Ok, everyone! Here are 5 questions about Rational Expression in Algebra.. answer what you want, don't answer what you don't want And if you only provide equations, or how to set the problems up, that works too! And thanks in advance!

1) Two savings accounts pay interest rates that differ by 1%. Equal amounts of money were invested in each account for a year. One account returns \$200 in interest and the other returns \$225. What is the higher interest rate?

2) A woman rides a unicorn 5 mph faster than she can ride a bicycle. She rides the unicorn 24 miles and rides a bicycle back in 11 hrs. About how fast does she ride the bicycle? (Because, you know, they are busy teaching me about practical applications of algebra in real life.. )

3) A black lab that can doggie paddle 3 mph in still water, paddles 10 miles downstream. Assuming the dog doesn't drown, he returns upstream in a total of 12 hours. Find the speed of the current.

4) Two certificates of deposit pay interest rates that differ by 4%. For the first CD, the money is invested for a year and earns \$480 interest. For the second CD the same amount of money invested earns \$800 in a year. What is the interest rate of the first CD account (rounded to the nearest tenth)?

5) Two savings accounts pay interest rates that differ by 1%. Equal amounts of money were invested in each account for a year. One account returns \$200 in interest and the other returns \$225. What is the lower interest rate?

Last edited by skipjack; April 26th, 2017 at 01:08 AM.
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April 25th, 2017, 11:52 PM   #2
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April 26th, 2017, 08:59 AM   #3
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Quote:
Originally Posted by Indigo28 View Post
Ok, everyone! Here are 5 questions about Rational Expression in Algebra.. answer what you want, don't answer what you don't want And if you only provide equations, or how to set the problems up, that works too! And thanks in advance!

1) Two savings accounts pay interest rates that differ by 1%. Equal amounts of money were invested in each account for a year. One account returns \$200 in interest and the other returns \$225. What is the higher interest rate?
Let the lower rate be r. Then the higher rate is r+ 0.01. Let A be the amount invested. Then rA= 200 and (r+ 0.01)A= 225. Dividing the second equation by the first, the A is eliminated and we have (r+ 0.01)/r= 225/200. Solve that equation for r. Since I hate fractions the first thing I would do is multiply both sides of the equation by 200r.

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2) A woman rides a unicorn 5 mph faster than she can ride a bicycle. She rides the unicorn 24 miles and rides a bicycle back in 11 hrs. About how fast does she ride the bicycle? (Because, you know, they are busy teaching me about practical applications of algebra in real life.. )
Let v be the speed, in miles per hour, at which she bicycles. Then she "unicorns" at v+ 5. The time taken to go 24 miles on the unicorn is 24/(v+ 5) and the time taken to return on the bicycle is 24/v. The total time is 24/(v+ 5)+ 24/v= 11 hours. Solve that equation for v. Get rid of the fractions by multiplying both sides by v(v+ 5).

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3) A black lab that can doggie paddle 3 mph in still water, paddles 10 miles downstream. Assuming the dog doesn't drown, he returns upstream in a total of 12 hours. Find the speed of the current.
Let s be the speed of the current in mile per hour. The dog's speed, relative to the bank, downstream, is 3+ v and, upstream, 3- v. It will take the dog 10/(3+ v) hours to swim 10 miles downstream and 10/(3- v) hours to swim back 10 miles upstream. The total time is 10/(3- v)+ 10/(3+ v)= 12. Again, get rid of the fractions by multiplying both sides of the equation by (3- v)(3+ v).

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4) Two certificates of deposit pay interest rates that differ by 4%. For the first CD, the money is invested for a year and earns \$480 interest. For the second CD the same amount of money invested earns \$800 in a year. What is the interest rate of the first CD account (rounded to the nearest tenth)?

5) Two savings accounts pay interest rates that differ by 1%. Equal amounts of money were invested in each account for a year. One account returns \$200 in interest and the other returns \$225. What is the lower interest rate?
These last two problems are exactly the same as problem one!
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April 26th, 2017, 09:50 PM   #4
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(1). The wording "the other returns \$225" was probably intended to mean "the other returns \$225 in interest". The given amounts differ by \$25, which is 1% of \$2500. The higher returned amount of interest is \$225, which is 9% of \$2500.
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April 30th, 2017, 06:40 PM   #5
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Thanks everyone! Your help is much appreciated! (And for the record, I agree with your thoughts on fractions, Country Boy )
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