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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 h…
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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 h…
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Mar 26, 2019
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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
Mathematics
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Bryan Olivier
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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! :)
Dan Wich
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Mar 30, 2019
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Dan Wich
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