Question 1005375
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8 {{{highlight(women)}}} and 12 girls can paint a large mural in 10 hours. 6 {{{highlight(women)}}} and 8 girls can paint the same mural in 14 hours. 
How long it would take to paint the mural one {{{highlight(woman)}}}? How long it would take to paint the mural one girl? 
* The answer has to be linear equation: reduction, equalization or replacement.
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Let w = number of hours it would take to paint the mural one woman.
Let g = number of hours it would take to paint the mural one girl.

Then one woman paints {{{1/w}}} of the mural per hour. 8 women paint {{{8/w}}} of the mural per one hour.
One girl paints {{{1/g}}} of the mural per hour. 12 girls paint {{{12/g}}} of the mural per one hour.

In this way you get the system of two equations 

{{{8/w}}} + {{{12/g}}} = {{{1/10}}},   (1)

{{{6/w}}} + {{{8/g}}} = {{{1/14}}}.    (2)

for two unknowns w and g. To solve it, multiply equation (1) by 2 (both sides) and equation (2) by -3, then add.
Thus you exclude the variable g and get an equation for the variable w only:

{{{16/w - 18/w}}} = {{{2/10 - 3/14}}},   or

{{{-2/w}}} = {{{14/70 - 15/70}}} = {{{-1/70}}}.

It gives w = 140. Hence, it takes 140 hours for 1 woman to paint the mural.

Now please complete the solution yourself.
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