Question 703290: Margarita is 5 feet 4 inches tall. She casts a shadow that is 8 feet.When her younger brother Amado stands in the same spot, he casts a shadow that is 1 inch less that margaritas height.
How tall is Amado ?
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! It would help to draw a diagram representing the information in this problem. We must understand that by geometry the two shapes we draw will be similar, and thus the sides will be proportionate. The proportion we set up for this problem consists of two fractions: The first must represent the ratio of both people's height, and the second must represent the ratio of the both people's shadow length. That is, Margarita's height must be in a fraction with Amado's height, and their shadow lengths must be in a fraction together. It does not matter which person's information we use, but we must keep it consistent throughout. (If we use Amado's information for height first in a fraction, which would indicate the numerator, then Amado's shadow length must be the numerator of the second fraction.) Finally, the units we use for measurement must remain consistent throughout. If we convert feet into inches, then we must change all of the measurements that are in feet into inches. (We must be mindful of what the problem asks for. Many times we need to write an answer in a specific unit.) Let us begin plugging values into a proportion.
For our sake, let us make the proportion (Amado's height)/(Margarita's height) = (Amado's shadow)/(Margarita's shadow). Margarita's information can come first, but let us do it this way. We already know Margarita's height and shadow length. Before we plug any values into our proportion places, let us convert her information from feet into inches. She has a height of 5 ft 4 in, or 64 inches. Her shadow is 8 ft, or 72 inches. Now let us plug this information into our proportion:
(Amado's height)/(Margarita's height) = (Amado's shadow)/(Margarita's shadow)
(Amado's height)/(64) = (Amado's shadow)/(72).
Amado's information is a little more difficult to decipher. We know that his shadow length is 1 inch less than Margarita's height. If Margarita's height is 64 inches, then we know that Amado's shadow is 64 - 1 or 63 inches (1 inch less than Margarita's height, which is 64 inches, thus Amado has 63 inches for shadow length). We cannot tell what Amado's height is directly from any information given in the problem. Therefore, we will use a variable for his height because it is unknown to us at this point:
(Amado's height)/(Margarita's height) = (Amado's shadow)/(Margarita's shadow)
(Amado's height)/(64) = (Amado's shadow)/(72)
x/64 = 63/72.
Now we can cross multiply to solve for this proportion:
x/64 = 63/72
63(64) = 72(x)
4032 = 72x
56 = x
x = 56 inches.
Remember that we must keep the label the same (inches). We have found how tall Amado is. If the problem wants us to give the answer in ft (I'm assuming not because it wasn't stated), then it would be 4 and 2/3 ft.
It is also possible to set the proportion like this:
(Amado's height)/(Amado's shadow) = (Margarita's height)/(Margarita's shadow).
The heights must be the numerator and the shadows must be the denominators. (They must show some sort of similarity.) We could also make the shadow come first, but it must come first in both fractions. We'd still get 56 inches as an answer.
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