Question 125379: Hi turor,
One more time I going to need your help. Thanks and god bless you.
1)The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimension would the length and width have the golden ratio?
2)Work. Henry sold 120 magazine subscriptions in X + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?
3)Barn painting. Melanie can paint a certain barn by herself in X days. Her helper Melissa can paint the same barn by herself in X days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for X = 5
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1)The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimension would the length and width have the golden ratio?
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length/ width = 8/5
Your Problem:
Let width be "x" ft ; then length is "x+2" ft
(x+2)/x = 8/5
Cross-multiply to get:
5x+10 = 8x
3x = 10
x = 3 1/3 ft. (width)
x+2 = 5 1/3 ft. (length)
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2)Work. Henry sold 120 magazine subscriptions in X + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?
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On the average he sells 120/(x+2) magazines per day.
In a week he would sell 7(120/(x+2) = 840/(x+2)
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Your 2nd sentence makes me think you left something out
of the problem description.
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3)Barn painting. Melanie can paint a certain barn by herself in X days. Her helper Melissa can paint the same barn by herself in X days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for X = 5
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Melanie DATA;
Time = x days/job : rate = 1/x jobs/day
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Melissa DATA:
Time = x days/job ; rate = 1/x jobs/day
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Together DATA:
Time = y days/job ; rate = 1/y jobs/day
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EQUATION:
1/x + 1/x = 1/y
2/x = 1/y
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Since they do 1/y job/day, they do (2/x) jobs/day
If x= 5, together they do (2/5) job per day.
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Cheers,
Stan H.
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