Question 783791
Most important goal is form two simultaneous equations in two variables.


x = count of hats
y = count of ties


Account for the cost: {{{15x+20y=250}}}
This should immediately be simplified so it is easier to use in solving the system.  Divide left and right by 5>....
{{{3x+4y=50}}}


Account for total quantity of items bought:  {{{x+y=15}}}


Solve this system in any way you want:
{{{highlight(3x+4y=50)}}}
{{{highlight(x+y=15)}}}





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recommendation:  multiply the "15" equation by 3, and then subtract from the "50" equation; and immediately find value for y....