SOLUTION: Please help me solve this word problem: In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium-size frames and 2 large ones for

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Question 697798: Please help me solve this word problem:
In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium-size frames and 2 large ones for $56. Shelly bought a small, a medium, and a large frame for $30. Write and solve a system of equations to find the price of each picture frame.
So far I have 2x+z=28 and 3y+2z=56 and x+y+z=30 with x being equal to the price of a small frame, y being the price of a medium one, and z being the price of a large one but I do not know how to solve it.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
In a souvenir shop, Jodi purchased 2 small picture frames and 1 large one for $28.
Mike bought 3 medium-size frames and 2 large ones for $56.
Shelly bought a small, a medium, and a large frame for $30.
Write and solve a system of equations to find the price of each picture frame.
:
You have to jump thru a few hoops to get to this one, elimination & substitution
:
Write an equation for each person's purchase using your variables
2x + 0y + z = 28
0x + 3y + 2z = 56
x + y + z = 30
:
Subtract the 3rd equation from the 1st
2x + 0y + z = 28
x + y + z = 30
--------------------eliminates z
x - y = -2
x = y - 2
:
Rearrange the 2nd equation
3y + 2z = 56
2z = (56-3y)
z =
:
in the first equation
2x + 0y + z = 28
replace x and z
2(y-2) + = 28
2y - 4 + = 28
multiply by 2
2(2y-4) + 56 - 3y = 56
4y - 8 + 56 - 3y = 56
4y - 3y + 48 = 56
y = 56 - 48
y = $8 for the medium frame
:
find z using the 2nd equation
3(8) + 2z = 56
24 + 2z = 56
2z = 56 - 24
2z = 32
z = $16 for the large frame
:
You can use the 3rd equation to find x now