Question

there were 180 people at a civic club fundraiser. members paid 4.50 per ticket, no members paid 8.25 per ticket. if the total receipts amounted to 1222.50 how many members and how many nonmembers attended the fundraiser

Answer 1

x= # of members
y= # of nonmembers

QUANTITY EQUATION
x + y= 180

COST EQUATION
$4.50x + $8.25y= $1222.50


STEP 1:
Use substitution or elimination to solve. I'm using elimination. Multiply quantity equation by -4.50 to eliminate the x term and solve for y.

-4.50(x + y)= -4.50(180)
-4.50x - 4.50y= -810


STEP 2:
Add the cost equation and the step 1 equation together. The x term is cancelled and we solve for y.

$4.50x + $8.25y= $1222.50
-4.50x - 4.50y= -810

3.75y= 412.50
divide both sides by 3.75

y= 110 nonmembers


STEP 3:
Substitute the y value into either original equation to solve for x.

x + y= 180

x + 110= 80
subtract both sides by 110

x= 70 members


CHECK:
use the opposite equation as chosen for step 3.

$4.50x + $8.25y= $1222.50
4.50(70) + 8.25(110)= 1222.50
315.00 + 907.50= 1222.50
1222.50= 1222.50 √


ANSWER: There were 70 members and 110 nonmembers attending.

Hope this helps! :)