Question

The length of Adriana's chicken coop is 3x + 12 feet. The length of her garden is 6x - 16 feet. The garden is the length of the chicken coop. What are the lengths of the chicken coop and the garden?

Answer 1

Given that the chicken coop and the garden are the same length, we have the following equation:

`3x+12=6x-16`

So, we need to solve for x to find out the length of both of them:

`\begin{gathered} 3x+12=6x-16 \\ \Rightarrow12+16=6x-3x \\ \Rightarrow28=3x \\ \Rightarrow x=(28)/(3) \end{gathered}`

we have that x=28/3. Now lets substitute this value on the equations to get the length of the chicken coop and the garden:

`\begin{gathered} x=(28)/(3) \\ \text{Chicken coop:} \\ 3((28)/(3))+12=28+12=40ft \\ \text{Garden:} \\ 6((28)/(3))-16=2(28)-16=56-16=40ft \end{gathered}`