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?

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 Link

Evadin2019 Evadin2019 · Answer 2 · 2019-10-07T21:34:41+02:00

Sarah's wire is [tex]1\frac{1}{7}[/tex] 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:

[tex]\frac{1}{2} x = \frac{2}{5} y[/tex] ................... (1)

[tex]z= 3x[/tex] ................... (2)

[tex]x+y+z = 6[/tex] .................... (3)

All of the three equation have 'x' variable, we are going to change the first equation:

[tex]\boxed {\frac{1}{2} x = \frac{2}{5} y }\\\boxed {y = \frac{1}{2}x \times\frac{5}{2} = \frac{5}{4}x }[/tex]

so we can write the third equation :

[tex]\boxed {x+y+z = 6 }\\\boxed {x + \frac{5}{4}x + 3x = 6}[/tex]

we are going to find the common denominator for this equation which is 4:

[tex]\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} }[/tex]

We get the result that Sarah's wire is [tex]1\frac{1}{7} feet[/tex]

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Keywords: multiplication, division, fraction, mixed fraction, Sarah's wire in feet, three variable equation, program linear, part to whole relationship