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Question 186610: i need help with the following word problem:
a museum charges $10 for a regular admission ticket, but members recieve a discount of $3 and students are admitted for $5. Last saturday, 750 tickets were sold for a total of $5400. if more 20 student tickets than regular tickets were sold, how many of each type of ticket were sold?
thanks!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! museum charges $10 for a regular admission ticket, but members receive a discount
of $3 and students are admitted for $5. Last Saturday, 750 tickets were sold for
a total of $5400. if more 20 student tickets than regular tickets were sold,
how many of each type of ticket were sold?
:
Let x = no. of reg tickets ($10)
Let y = no. of member ticket ($7)
Let z = no. of students ($5)
:
No. of tickets equation:
x + y + z = 750
:
Total$ equation
10x + 7y + 5z = 5400
:
"20 student tickets than regular tickets were sold,"
z = (x+20)
:
We know y = 750 - x - z; substitute (x+20) for z
y = 750 - x - (x+20)
y = 750 - 2x - 20
y = (730 - 2x)
:
Substitute for y and z in the Total$ equation, find x:
10x + 7(730-2x) + 5(x+20) = 5400
Get rid of the brackets
10x + 5110 - 14x + 5x + 100 = 5400
10x - 14x + 5x + 5210 = 5400
x = 5400 - 5210
x = 190 reg tickets
:
y = 730 - 2x
y = 730 - 380
y = 350 member tickets
:
z = x + 20
z = 190 + 20
z = 210 students tickets
;
:
Check solutions in both equations
190 + 350 + 210 = 750
and
10(190) + 7(350) + 5(210) =
1900 + 2450 + 1050 = $5400
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