SOLUTION: 14.Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. You are putting a stone border of uniform width around a rectangular gar

Question 302419: 14.Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
You are putting a stone border of uniform width around a rectangular garden that measures 6 yards by 15 yards. You only have enough stone to cover 100 square yards. How wide should the border be?

Found 2 solutions by london maths tutor, josmiceli:
Answer by london maths tutor(243) (Show Source): You can put this solution on YOUR website!
Let's the stone border width be x
The width including stone border = 6 + x + x = 6 + 2x
The length including stone boarder = 15 + x + x = 15 + 2x
Area of the garden = 6*15 = 90 yards^2
Area of the garden and stone border = (6+2x)*(15+2x)
The difference of the two area is 100 yards^2
Therefore:
[(6+2x)*(15+2x)] - 90 = 100
(90 + 12x + 30x + 4x^2) - 90 = 100
4x^2 + 42x - 100 = 0
2x^2 + 21x - 50 = 0
Using the formular :
where a = 2 , b = 21 and c = -50
x = 2 yard or - 12.5 yards(N/A)
Answer: The width of the path way is 2 yards.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
I'm not familiar with the 5-step process, but I
can show you how I'd do it
Let = the width of the border
The area of the garden is yd2
The dimensions of the garden + border are:
by
The area of the garden + border is

The area of the garden is yd2
The area of the border is yd2

Solve using quadratic formula

(there's another solution, but it's negative)

The border around the garden is 2 yds wide
check:

OK
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