SOLUTION: There were 233 tickets sold for a basketball game. The activity cardholder's tickets cost $150 and the non-cardholders' tickets cost $2.25. The total of money collected was $384.75

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Question 146137: There were 233 tickets sold for a basketball game. The activity cardholder's tickets cost $150 and the non-cardholders' tickets cost $2.25. The total of money collected was $384.75. How many of each kind of ticket were sold?
How many cardholder's tickets were sold?
How many non-cardholders' tickets were sold?






Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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There were 233 tickets sold for a basketball game. The activity cardholder's tickets cost $1.50 and the non-cardholders' tickets cost $2.25. The total of money collected was $384.75. How many of each kind of ticket were sold?
:
Let x = no. cardholders
Let y = no. of non-cardholders
:
"There were 233 tickets sold for a basketball game."; an equation for this:
x + y = 233
y = (233-x)
:
The total collected was 384.75
1.50x + 2.25y = 384.75
;
How many cardholder's tickets were sold?
:
substitute (233-x) for y in the above equation
1.5x + 2.25(233-x) = 384.75
1.5x + 524.25 - 2.25x = 384.75
1.5x - 2.25x = 384.75 - 524.25
-.75x = -139.50
x = %28-139.50%29%2F%28-.75%29
x = +186 cardholders
:
:
How many non-cardholders' tickets were sold?
:
y = 233 - 186
y = 47 non-cardholders
:
:
Check solutions
1.5(186) + 2.25(47) = 384.75