Sarah's wire is \(1\frac{1}{7}\) feet.
Further Explanation
Given:
Let's say that:
Sarah's wire = x
Daniel's = y
Chris = z
From the problem given we have got 3 equation as follow:
\(\frac{1}{2} x = \frac{2}{5} y\) ................... (1)
\(z= 3x\) ................... (2)
\(x+y+z = 6\) .................... (3)
All of the three equation have 'x' variable, we are going to change the first equation:
\(\boxed {\frac{1}{2} x = \frac{2}{5} y }\\\boxed {y = \frac{1}{2}x \times\frac{5}{2} = \frac{5}{4}x }\)
so we can write the third equation :
\(\boxed {x+y+z = 6 }\\\boxed {x + \frac{5}{4}x + 3x = 6}\)
we are going to find the common denominator for this equation which is 4:
\(\boxed {\frac{4x +5x+12x}{4} = 6 }\\ \boxed {\frac{21x}{4} = 6 }\\ \boxed {21x = 24 } \\\boxed {x= \frac{24}{21} = 1\frac{7}{21} = 1\frac{1}{7} }\)
We get the result that Sarah's wire is \(1\frac{1}{7} feet\)
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Keywords: multiplication, division, fraction, mixed fraction, Sarah's wire in feet, three variable equation, program linear, part to whole relationship
