SOLUTION: Standing next to each other, a woman casts a 46.9 inch shadow and her 50 inch tall daughter casts a 35 inch shadow. What is the height of the woman to the nearest inch? I tried

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Question 106195: Standing next to each other, a woman casts a 46.9 inch shadow and her 50 inch tall daughter casts a 35 inch shadow. What is the height of the woman to the nearest inch?
I tried forming a ratio between the woman and the daughter
x:46.9= 50: 35
is this the right way to do it? if not, how can I proceed with the question?
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
That is the way to do the problem. You set up the proportion as:
.
Actual height of woman is to woman's shadow as actual height of daughter is to daughter's
shadow.
.
Since the actual height of the woman is unknown you let x be that height. Then your proportion
became:
.

.
You can solve this by cross multiplying. Multiply the numerator of the first ratio (x) by the
denominator of the second ratio (35). Set it equal to the product you get when you multiply
the denominator of the first ratio (46.9) times the numerator of the second ratio (50).
.
Can you see why this is called cross multiplying? It is because if you draw lines that
connect the numbers you are multiplying, it forms a cross that is centered on the equal sign.
.
Anyway, when you cross multiply you get:
.
35x = (46.9)*(50)
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The right side multiplies out to 2345. So the equation is reduces to:
.
35x = 2345
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Solve for x by dividing both sides by 35. Your answer when you do that division is the height
of the woman in inches. So don't forget to label your answer "inches".
.
Hope this helps you and shows you how you can solve proportions (two ratios that are equal)
by cross multiplying. When you use cross multiplying it will work regardless of which
numerator or denominator is the unknown x.
.
Keep up the good work.
.