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Question 697753: In a souvenier shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium 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 size of picture frame.
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In a souvenier shop, Jodi purchased 2 small picture frames and 1 large one for $28. Mike bought 3 medium 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 size of picture frame.
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Equations:
2s + L = 28
3m + 2L = 56
s + m + L = 30
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Substitute for "s" and for "m" ; solve for "L":
s = (-L/2)+14
m = (-2/3)L + (56/3)
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(-L/2) + 14 + (-2/3)L + (56/3) + L = 30
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Multiply thru by 6 to get:
-3L + 84 -4L + 112 + 6L = 180
-L + 196 = 180
-L = -16
L = 16 (# of large frames)
s = -8+14 = 6 (# of small frames)
m = (-2/3)(16)+(56/3) = 8 (# of medium frames)
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Cheers,
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Stan H.
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