SOLUTION: 2/5 of the cost of a guitar is equal to 1/4 of the cost of a violin. If the violin costs $2870 more than the guitar, what is the cost of both musical instruments?

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Question 279199: 2/5 of the cost of a guitar is equal to 1/4 of the cost of a violin. If the violin costs $2870 more than the guitar, what is the cost of both musical instruments?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2/5 of the cost of a guitar is equal to 1/4 of the cost of a violin. If the violin costs $2870 more than the guitar, what is the cost of both musical instruments?
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Equations:
(2/5)g = (1/4)v
v = g + 2870
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Rearrange the 1st equation:
Multiply thru by 20 to get:
8g = 5v
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Substitute for "v" and solve for "g":
8g = 5(g+2870)
8g = 5g+14350
3g = 14350
g = 4783.33 (price of the guitar)
v = 4783.33 + 2870 = 7653.33 (price of the violin)
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Cheers,
Stan H.