# SOLUTION: 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

Algebra ->  Algebra  -> Rectangles -> SOLUTION: 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      Log On

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 Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth

 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(57377)   (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? -------------- 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) ---------------------------- 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? ----- On the average he sells 120/(x+2) magazines per day. In a week he would sell 7(120/(x+2) = 840/(x+2) ----------- Your 2nd sentence makes me think you left something out of the problem description. ------------- 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 ------- Melanie DATA; Time = x days/job : rate = 1/x jobs/day ------------------ Melissa DATA: Time = x days/job ; rate = 1/x jobs/day ------------------ Together DATA: Time = y days/job ; rate = 1/y jobs/day ------------------- EQUATION: 1/x + 1/x = 1/y 2/x = 1/y -------------- Since they do 1/y job/day, they do (2/x) jobs/day If x= 5, together they do (2/5) job per day. ============== Cheers, Stan H.