Question 1112145
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The given information tells us...
{{{x+y+z = 800}}}  (1)
{{{x+(1/2)y+(2/5)z = 400}}}  (2)
{{{(3/4)x+y+(1/4)z = 400}}}  (3)<br>
Solve the system by first eliminating one variable to reduce the problem to two equations in two variables.  With the given coefficients, eliminating y first looks to be the easiest.<br>
{{{x+y+z = 800}}}; {{{2x+y+(4/5)z = 800}}}; --> {{{-x+(1/5)z = 0}}}<br>
{{{x+y+z = 800}}}; {{{(3/4)x+y+(1/4)z = 400}}}; --> {{{(1/4)x+(3/4)z = 400}}}  -->  {{{x+3z = 1200}}}<br>
Adding the last two equations,
{{{(16/5)z = 1600}}}  -->  {{{z = 500}}}<br>
Plugging back into earlier equations, x=100 and y=200.<br>
CHECK:
{{{100+200+500 = 800}}}
{{{100+(1/2)200+(2/5)500 = 100+100+200 = 400}}}
{{(3/4)(100)+200+(1/4)(500) = 75+200+125 = 400}}}