Question

Determine the width of the garden. Nina must put 60 feet of fencing around her rectangular garden. The length of the garden is three feet longer than twice the width. What is the solution set for 2w + 2(2w + 3) = 60 given the replacement set {6, 7, 8, 9}?

Answer 1

9 is a solution.

Explanation:

The replacement set is the set of values that can be substituted in the equation (for the variables).

Given a replacement set, we need to substitute every value of the set in our equation and see if the equation holds for that value. If it does, then the value is a solution of the equation.

In this problem we have the equation 2w + 2(2w + 3) = 60 and the replacement set is {6,7,8,9}

We are going to start replacing the different values of the set.

• w = 6

`2w + 2(2w + 3) = 60\\2(6) + 2(2(6)+3) = 60\\12 + 2(12+3) = 60\\12 + 2(15) = 60\\12 + 30 \\eq 60`

Thus, 6 is not a solution.

• w = 7

`2w + 2(2w + 3) = 60\\2(7) + 2(2(7) +3) = 60\\14 + 2 (14+3) =60\\14 + 2(17)=60\\14+34=60\\48 \\eq 60`

Thus, 7 is not a solution.

• w = 8

`2w + 2(2w + 3) = 60\\2(8) + 2(2(8)+3) = 60\\16 + 2(16+3)=60\\16 +2 (19) =60\\16 + 38 \\eq 54`

Thus, 8 is not solution.

• w = 9

`2w + 2(2w + 3) = 60\\2(9) + 2(2(9) + 3) =60\\18 + 2 (18+3) =60\\18 +2(21)=60\\60=60`

Thus, 9 is a solution.

Answer 2

2w+2(2w+3)=60

2w+4w+6=60

6w+6=60

6w=54

w=54/6 =9

the width is 9 feet