SOLUTION: A boy who is 4 feet 6 inches tall casts a shadow that is 6 feet 3 inches long. What is the height of a tree that casts a shadow that is 25 feet long? I know that it is direct va

Question 540746: A boy who is 4 feet 6 inches tall casts a shadow that is 6 feet 3 inches long. What is the height of a tree that casts a shadow that is 25 feet long?
I know that it is direct variation and that I need to use the equation y=kx. In my instruction, however, there were only example problems in which x was changed. I may be completely off base but I assumed that I could do the equation as followed:
y(height of boy)=4.6; x(shadow)=6.25
solve for y=6.25
y(k)=x
k(25)=6.25
k(25)/6.25 = 6.25/6.25
k=4
4.6 (4) = x
x=18.4
18 is an answer... but that doesn't seem right.
And then I realized that something terribly wrong happened. Thank you so much to who ever might decide to help!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
x and y represent an object and its shadow
___ it makes no difference which letter represents which parameter, as long as you are consistent
___ yes, this is a direct variation; bigger objects have bigger shadows

let x be the object and y the shadow
___ work in consistent units ___ feet, in this case

6.25 = k * 4.5 ___ k = 6.25 / 4.5

25 = k * x ___ 25 / k = x ___ 25 / (6.25 / 4.5) = x ___ 18 = x

you did find the right answer, but your technique needs work (you were lucky...)
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