On a sunny day, Madelyn notices that her shadow is 51 inches long. If it is 85 inches from the top of her head to the end of the shadow, how tall is Madelyn?
To determine Madelyn's height, we can set up a proportion using the lengths of her shadow and her actual height.
Let x be Madelyn's height.
Thus, we can set up the following proportion:
\( \frac{51}{x} = \frac{85}{85 + x} \)
Cross multiplying, we get:
\( 51(85 + x) = 85x \)
\( 4335 + 51x = 85x \)
Subtracting 51x from both sides:
\( 4335 = 34x \)
Dividing by 34:
\( x = \frac{4335}{34} \)
x ≈ 127.5
Madelyn is approximately 127.5 inches tall.