SOLUTION: After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135

Question 1136973: After watching a major musical production at the theater, the patrons can purchase souvenirs. If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.
A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175. Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75. What is the cost of each item?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
After watching a major musical production at the theater, the patrons can purchase souvenirs.
If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135.
A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175.
Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75.
What is the cost of each item?
:
let t = price of T shirts
let v = price of video
let a = price of stuffed animal
:
Write an equation for each statement
" If a family purchases 6 t-shirts, the video, and a stuffed animal, their total is $135."
6t + v + a = 135
"A couple buys 2 t-shirts, the video, and 5 stuffed animals for their nieces and spends $175."
2t + v + 5a = 175
"Another couple buys 2 t-shirts, the video, and a stuffed animal, and their total is $75."
2t + v + a = 75
:
Using the 2nd and 3rd equations find a
2t + v + 5a = 175
2t + v + a = 75
-----------------subtraction eliminates t and v, find a
4a = 100
a =100/4
a = $25 for the animal
:
Using the 1st and 2nd equations, substitute 25 for a
6t + v + 25 = 135
6t + v = 110, subtracted 25 from both sides
and
2t + v + 5(25) = 175
2t + v = 50, subtracted 125 from both sides
:
Using elimination on these two equations
6t + v = 110
2t + v = 50]
--------------subtraction eliminates v, find t
4t = 60
t = 60/4
t = $15 for T shirts
:
Find v using the 3rd equation,
2(15) + v + 25 = 75
v = 75 - 30 - 25
v = 75 - 55
v = $20 for each video
:
:
Check solutions in the 1st equation
6(15) + 20 + 25 = 175
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