SOLUTION: Two hockey tickets and one basketball ticket cost $110.40. One hockey ticket and two basketball tickets cost $106.32. What is the price of each ticket? PLEASE HELP ME SOLVE THIS

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Question 1123684: Two hockey tickets and one basketball ticket cost $110.40. One hockey ticket and two basketball tickets cost
$106.32. What is the price of each ticket?
PLEASE HELP ME SOLVE THIS QUESTION
Found 2 solutions by Theo, MathLover1:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let h = the price of one hockey ticket.
let b = the price of one baseball ticket.

your equations are:

2h + b = 110.40
1h + 2b = 106.32

thse are two equations that need to be solved simultaneously because the same value of h and b will apply equally to each equation.

multiply both sides of the first equation by 2 and leave the second equation as is to get:

4h + 2b = 220.80
1h + 2b = 106.32

subtract the equation from the first to get 3h = 114.80

solve for h to get h = 114.80 / 3 = 38.16

replace h with 38.16 in the second equation and solve for b as shown below.

1 * 38.16 + 2b = 106.32
subtract 38.16 from both sides of the equation to get:
2b = 68.16
solve for b to get b = 68.16 / 2 = 34.08

you have h = 38.16 and b = 34.08

that's your solution.

replace h and b in the original equations to confirm the solution is correct.

2h + b = 110.40 becomes 2*38.16 + 34.08 = 110.40 which becomes 110.4 = 110.4, confirming the solution is correct in the first equation.

1h + 2b = 106.32 becomes 1*38.16 + 2*34.08 = 106.32 which becomes 106.32 = 106.32, confirming the solution is correct in the second equation.

your solution is that the price of one hockey ticket is 38.16 and the price of one baseball ticket is 34.08.





Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let's hockey tickets be x and basketball tickets y

if given that two hockey tickets and one basketball ticket cost $110.40, we have
2x%2By=110.40....eq.1
if one one hockey ticket and two basketball tickets cost $106.32, we have
x%2B2y=106.32....eq.2
now solve this system
start with 2x%2By=110.40....eq.1, solve for y
y=110.40-2x....substitute in x%2B2y=106.32....eq.2
x%2B2%28110.40-2x%29=106.32....solve for x
x%2B220.80-4x=106.32
220.80-3x=106.32
220.80-106.32=3x
114.48=3x
x=114.48%2F3
x=38.16 -> one hockey tickets costs highlight%2838.16%29

now, go to y=110.40-2x, plug in 38.16 for x
y=110.40-2%2A38.16
y=110.40-76.32
y=34.08-> one basketball tickets costs highlight%2834.08%29