SOLUTION: When Allen and Maggie reached retirement, they were finally able to buy the house of their dreams. It had a 40 by 72 foot rectangular yard. Maggie cultivated 5/12 of the area in fl
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Question 600786: When Allen and Maggie reached retirement, they were finally able to buy the house of their dreams. It had a 40 by 72 foot rectangular yard. Maggie cultivated 5/12 of the area in flowers, which she grew in an even rectangular border around the central court. Every morning Allen walked the dog around the central grass area just in side of the flowers. How many laps did he have to do to walk at least 1/4 mile?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the width of the border. Since the border goes all the way around the garden, the length and width of the lawn area are both reduced by 
each. Hence, the area of the lawn part is given by
(70\ -\ 2x))
The area of the original yard is 40 times 72 which is 2880. If the flower bed part is 5/12 of the original area, then the remaining lawn part has to be 7/12 of the original value. Hence:
(70\ -\ 2x)\ =\ 2880\ \times\ \frac{7}{12})
Simplify and solve the quadratic for . Then calculate 
and 
which are the dimensions of the inner lawn. Using these dimensions, calculate the perimeter of the inner lawn. There are 5280 feet in a statute mile. Divide by 4 to get the number of feet in 1/4 mile. Divide the number of feet in 1/4 mile by the perimeter of the inner lawn area. Round up to the nearest whole lap.
John
My calculator said it, I believe it, that settles it
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