SOLUTION: Your neighbor has put in a 18 by 51 foot garden along the whole back end of their back yard. This reduced the back yard lawn area by 24%. What are the total dimensions of his back

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Question 972505: Your neighbor has put in a 18 by 51 foot garden along the whole back end of their back yard. This reduced the back yard lawn area by 24%. What are the total dimensions of his back yard? What are the dimensions of the remaining lawn area?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
(Make a drawing of the situation to more easily analyze the problem.)

Let dimensions of yard be x and y, and 18 be part of the x and 51 be part of the y of the garden.

Yard Area, xy
Garden Area, 18%2A51.
Yard Area not containing garden,%28x-18%29%28y-51%29.

Ambiguous: Either "whole back end" is x=18 or it is y=51.

%28x-18%29%28y-51%29, the reduced back yard area, 24% of total yard area.
highlight%28%28x-18%29%28y-51%29=0.24%28xy%29%29.

That ambiguous part can be used to decide which way x or y should be assigned. Each choice will give a quadratic equation in either x or y.

(Another exercise not responded with a complete solution; but just a strategy with part of the process.)

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Your neighbor has put in a 18 by 51 foot garden along the whole back end of their back yard.
This reduced the back yard lawn area by 24%.
What are the total dimensions of his back yard?
What are the dimensions of the remaining lawn area?
:
Find the area of the garden; 18 * 51 = 918 sq/ft
We know the width of the yard is 51 ft
let L = the total length of the yard including the garden
then
51L = the area of the whole yard
:
Find the length of the yard
24% of the whole yard = the garden area
.24(51L) = 918
12.24L = 918
L = 918/12.24
L = 75 ft is the length of the whole yard
therefore
75 by 51 is dimensions of the back yard
:
Find the dimensions of the remaining lawn
75 - 18 = 57 ft is length
57 by 51 is dimensions of the remaining lawn
:
:
:
See if this checks out,
find the overall area: 75 * 51 = 3825 sq/ft
find the area of the remaining lawn, add to the garden area
57 * 51 = 2907
2907 + 918 = 3825