Question

Half of Sarah's wire is equal to 2/5 of Daniel's. Chris has 3 times as much as Sarah. In all, their wire measures 6 ft. how long is Sarah's wire in feet?

Answer 1

Let x be the length of Daniel's wire. With the representation, Sarah's wire is 4x/5 and that of Chris is 3 time 4x/5. The equation that best represent the situation given above is,
                                       x + 4x/5 + 3(4x/5) = 6
The value of x in ft is 1.42. Therefore, Sarah's wire which is 4x/5 is approximately 1.14 ft long. 

Answer 2

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