John sold 30 tickets to the 4H Fish Fry. An adult ticket cost $7 and a child's ticket...

  • Thread starter Thread starter Erin B
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Erin B

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...cost $3. If John? collected $130, how many of each ticket did he sell? Set up systems of questions and solve

Please show your steps, my answers aren't matching up right =/
 
x = no. of adult tickets
y = no. of child tickets

x + y = 30 --------- (1)
7x + 3y = 130 -------(2)

Multiply equation (1) by 3 and solve (1) and (2)
3x+ 3y = 90
7x + 3y = 130
______________
-4x = -40
x = 10

plug this in (1)
y = 20
 
A = Adult, C = Child

#1. A + C = 30 total tickets sold
#2. $7A + $3C = $130

Solve for A in #1. A = 30 - C
Substitute (30 - C) into equation #2 for A.
7(30 - C) + 3C = 130 (remove the $ for simplicity)
210 - 7C + 3C = 130
-4C = -80
C = -80/-4

C = 20 children's tickets sold.
So, but deductive reasoning and subtraction, there were 10 Adult tickets sold.
 
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