Question 228538
180 people at a civic club fundraiser. Members pay $4.50 per ticket and NONmembers pay 8.25 per ticket. If total is $1,222.50 then how many members attended and how many non members attended.


Step 1.  Let x be the number of members.


Step 2.  Let 180-x be the number of nonmembers since there are 180 people.


Step 3.  Let 4.50x be the dollar value of tickets for members.


Step 4.  Let 8.25(180-x) be the dollar value of tickets for non-members.


Step 5.  Then, {{{4.50x+8.25(180-x)=1222.50}}} is the total value of tickets sold.


Step 6.  Solving {{{4.50x+8.25(180-x)=1222.50}}} yields the following steps.


{{{4.50x+1485-8.25x=1222.50}}}


{{{-3.75x+1485=1222.50}}}


Add 3.75x-1222.50 to both sides of the equation


{{{-3.75x+1485+3.75-1222.50=1222.50+3.75x-1222.50}}}


{{{262.50=3.75x}}}


Divide by 3.75 to both sides of the equation


{{{262.50/3.75=3.75x/3.75}}}


{{{70=x}}} and {{{180-70=110}}}


Check dollar value with these numbers:


{{{70*4.50+110*8.25=315.00+907.50=1222.50}}} which is a true statement.


Step 7.  ANSWER.  The number of tickets sold to members is 70 and the amount of tickets sold to non-members is 110.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J