Question 1146597
x, the slow machine
y, the fast machine
those rates in PARTS per HOUR


{{{system(28.2x+37.5y=27210,88.6x+66.5y=59830)}}}
Simplify and solve the system.


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A possible way but not the only way to start solving the system:

From first equation
{{{37.5y=27210-28.2x}}}
{{{y=(27210-28.2x)/37.5}}}


subst. to second equation
{{{88.6x+66.5((27210-28.2x)/37.5)=59830}}}

{{{88.6x+66.5(27210/37.5-28.2x/37.5)=59830}}}

{{{88.6x+66.5*27210/37.5-66.5*28.2x/37.5=59830}}}

{{{88.6x-66.5*28.2x/37.5=59830-66.5*27210/37.5}}}

{{{(88.6-66.5*28.2/37.5)x=59830-66.5*27210/37.5}}}

{{{x=(59830-66.5*27210/37.5)/(88.6-66.5*28.2/37.5)}}}

{{{x=300}}}

and you should be able to figure the rest and to finish.