Word problem help.

[Dillinger4]

A rectangular garden measures 5ft by 7ft and is surrounded by a uniform path x ft wide. If the total area of garden plus path is 63 sq ft, find the width of the path.

Im lost on this problem. Any help would be great.

Area of the garden should be (5 * 7) which gives 35 ft. 63 - 35 = 28. So the area of the path should equal 28 ft?

Im confused.

[DiGiTaIErRoR]

+++++++
+-----+
+-----+
+-----+
+-----+
+-----+
+-----+
+-----+
+++++++

+ = Path
- = Garden

9*7 = 63 so a 9*7 square is around the garden... it'd seem.

So the path is 1 foot across. Area of path, 28 sq. ft..

[Dillinger4]

This is what i come up with.

63 = (5 + 2y)(7 + 2y)
63 = 35 + 10y + 14y + 4y
63 = 35 + 24y + 4y
63 - 35 + 24y + 4y
28/28 = 28y/28
y = 1

Path = 1ft

[nishantp]

Originally posted by Dilenger4
This is what i come up with.

63 = (5 + 2y)(7 + 2y)
63 = 35 + 10y + 14y + 4y
63 = 35 + 24y + 4y
63 - 35 + 24y + 4y
28/28 = 28y/28
y = 1

Path = 1ft

That works for the wrong reason. The part I put in Bold should be 4y², which makes the whole thing a quadratic.

I didn't show all the steps but the algebraic solution is

63=(5+y)(7+y)
0 = y2 + 12y - 28

The roots are 2 and -14. The -14 is discarded.

Since the path adds 2 feet to both dimensions, but goes all the way around, the width of the path is 2/2=1ft.



PS - I deleted my earlier post because I made a mistake.