candygirl200:

Ben fenced his backyard using 350 feet of fencing. The width of his yard is 12 feet less than twice the length. Write an equation that can be used to determine the dimensions of his yard and solve.

3 weeks ago
Shadow:

Hello @candygirl200 Do you mind if I help you today?

3 weeks ago
candygirl200:

sure u could help

3 weeks ago
Shadow:

"The width of his yard is 12 feet less than twice the length." w = 2l - 12 Where, w = width l = length

3 weeks ago
Shadow:

Going to assume that this is a rectangular backyard (as they usually are). The formula for the perimeter of a rectangle can be written as, P = 2l + 2w Where P is the perimeter

3 weeks ago
Shadow:

Right now we have three variables. P, w, and l In order to solve for a variable in any algebraic equation, we must have only ONE unknown. "Ben fenced his backyard using 350 feet of fencing." With this sentence we know that P = 350ft as a fence goes around the "perimeter" Then with that information we start working some magic with our two equations that I showed. w = 2l - 12 P = 2l + 2w We will be using the second one as it expresses the dimensions of the yard in terms of the perimeter. We can replace P with 350ft 350ft = 2l + 2w We have w defined in our earlier equation, so we can do \[350ft = 2l + 2(2l - 12) \]

3 weeks ago
Shadow:

Are you with me so far?

3 weeks ago
candygirl200:

yes

3 weeks ago
Shadow:

\[350 = 2l + 2(2l - 12) \] We solve for our unknown, the length \[350 = 2l + 4l - 24\] \[350 = 6l - 24\] \[374 = 6l\] \[l = \frac{ 187 }{ 3 }\]

3 weeks ago
Shadow:

Where do you think we go from here?

3 weeks ago
candygirl200:

plug in to find w

3 weeks ago
Shadow:

Exactly. Which equation would we use?

3 weeks ago
candygirl200:

the original one

3 weeks ago
Shadow:

We can use both P = 2l + 2w and w = 2l - 12, but it is easier to use the second one since it is already in terms of w. \[w = 2l - 12\] \[w = 2(\frac{ 187 }{ 3 }) - 12\] \[w = \frac{ 374 }{ 3 } - 12\] \[w = \frac{ 374 }{ 3 } - \frac{ 36 }{ 3 }\] \[w = \frac{ 338 }{ 3 }\]

3 weeks ago
Shadow:

Do you understand how I got this?

3 weeks ago
candygirl200:

yes thanks

3 weeks ago
Shadow:

No problem :)

3 weeks ago