SOLUTION: This question is very hard and I get it wrong everytime so I hope you can help. A 90-foot tall lakefront hotel casts a showdow on the water. How long is the shawdow if a near

Algebra ->  Proportions  -> Lessons -> SOLUTION: This question is very hard and I get it wrong everytime so I hope you can help. A 90-foot tall lakefront hotel casts a showdow on the water. How long is the shawdow if a near      Log On


   

Question 118263: This question is very hard and I get it wrong everytime so I hope you can help.
A 90-foot tall lakefront hotel casts a showdow on the water.
How long is the shawdow if a nearby 10-foot tall basketball hoop casts a 7-foot shawdow?
PLEASE RESPOND AND THANKYOU!
Found 3 solutions by TP, jim_thompson5910, MathLover1:
Answer by TP(29) About Me  (Show Source):
You can put this solution on YOUR website!
Since the hotel is 9 times the height of the hoop then the hotel's shadow must be 9 times the length of the hoop's shadow.
So the length of the hotel's shadow is 9*7=63 feet.ANS

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of hotel's shadow

Notice there's a relationship between the height of the object and the length of the shadow. So we have this ratio:


x%2F90=7%2F10 Notice the shadow lengths are the numerators and the denominators are the objects heights.


x=%287%2F10%29%2A90 Multiply both sides by 90


x=630%2F10 Multiply


x=63 Simplify



So our answer is x=63


So the length of the hotel's shadow is 63 ft.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

90-foot+%3A+x+=+10-foot+%3A+7-foot

x+%2A10-foot+=90-foot%2A7-foot………divide by 10-foot

x+%2A10-foot%2F+10-foot+=%2890-foot%2A7-foot%29%2F+10-foot+………

………

x+=9%2A7-foot

x+=63-foot....lakefront hotel casts a 63-foot showdow on the water

Check:
90-foot+%3A++x-foot+=+10-foot+%3A+7-foot

90-foot+%3A++63-foot+=+10-foot+%3A+7-foot
1.4285714285714285714285714285714=1.4285714285714285714285714285714
1.43=1.43