Algebra

I need help with my daughters homework. I know a little bit of algebra but it has been about 15 years since I have done it. She switched schools recently and there was a learning gap in the schools. The problem is: give the demensions of rectangles with the perimeters of 70 feet and length-to-width ratios of 4 to 5. I hoping this could be done step by step so I can work it out and show her how to do it. Any help would be appreciated.

Let length be l, and w for width.

2L + 2W= perimeter or = 70
2W= 70 - 2L
W= 35 - L

Now, one knows the L/W ratio, so

L/W=4/5 and manipulating that
L= 4W/5

{Putting that in the above equation)
W= 35 - L = 35 - 4W/5
adding 4W/5 to both sides..
W+ 4W/5 =35
9W/5= 35
9W=35*5
W= 35*5/9= 19.4 feet
but L+ W= 35, so L= 35-19.4 feet

Check: Is L/W= 4/5 ?
15.6/18.4= .8, so it checks

Thank you so much!

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