Question

Hank is building a dog run for his dog. He wants the ratio of the length to the width of the dog run to be 5 : 2. If he builds the dog run so the length is 10.5 feet, which equation can be used to solve for the width, x? What is the value of x?

Answer 1

ratio of a length to width=5/2
l:x=5:2
l/x=5/2
l=5/2*x

L=10.5 feet
10.5*2/5=x
4.2 feet is width

Answer 2

The equation is
`\\ (5)/(2) : (10.5ft)/(x)`; The value of x is 4.2ft.

Explanation:

A ratio is like a constant that remains between two values, and we can use it to find whatever others that keep the same constant relation between them.

Hank wants a dog run that keeps a constant relation between length to the width. That is, the length must be 2.5 times to the width (
`\\ (5)/(2) = 2.5` ).

So, knowing that ratio or constant, we can represent it as follows:

`\\ (lenght)/(width) : (5)/(2) \\` [ 1 ]

But, it also could be expressed as the relation between the width to the length:

`\\ (width)/(length):(2)/(5)` [ 2 ]

He wants a lenght of 10.5ft for building a dog run for his dog, and that this new value must keep the ratio just explained [ 1 ] to the width expected.

So, the equation is:

`\\ (5)/(2) : (10.5ft)/(x)`

And we have to find the value for x that solve this equation.

However, we can use an easier way to represent this using the equation [ 2 ] for solving x :

`\\ (w)/(l) :(2)/(5) : (x)/(10.5ft) \\\\ x = (2 * 10.5ft)/(5)=4.2ft\\`

That is, the width must be 4.2ft to keep the ratio length to the width 5:2 ( or the ratio width to the length 2:5).

To check this answer:

`\\ (length)/(width) : (5)/(2) =2.5`

`\\ (length)/(width) = (10.5ft)/(4.2ft) = 2.5`.

`\\ (width)/(length) : (2)/(5) = 0.4\\`

`\\ (width)/(length) = (4.2ft)/(10.5ft) = 0.4`.