Question 205238: Martin purchases 2 apples and 4 oranges. Michelle purchases 8 apples and 2 oranges. If Michelle pays twice as much as Martin. How many apples can be purchased for the price of 9 oranges?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let cost of apples = x
let cost of oranges = y
let b = how much martin pays
let g = how much michelle pays
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b = 2x + 4y
g = 8x + 2y
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the assumption is that they both pay the same price per apple and the same price per orange.
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michelle pays twice as much as martin so:
g = 2*b
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if g = 2*b then:
8x +2y = 2*(2x + 4y)
this becomes:
8x + 2y = 4x + 8y
subtract 4x from both sides of the equation and subtract 2y from both sides of the equation to get:
8x - 4x = 8y - 2y
which results in:
4x = 6y
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the question is:
how many apples can be purchased for the price of 9 oranges.
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To find that you need to find the price of oranges in comparison to the price of apples.
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Since y is the price of oranges, then solve for y in the equation of:
4x = 6y
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Dividing both sides of this equation by 6 gets:
Y = 4x/6 = (2/3)*x
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The price of 9 oranges would then be 9 * y = 9 * (2/3)*x
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This results in (18/3) * x
Which reduces to:
6*x
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The price of 9 oranges is 6 apples.
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One way to check your answer is to place this results in the original equations and see what comes out.
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The original cost to Martin was:
2x + 4y
since y = (2/3)*x then this cost becomes:
2x + 4*(2/3)*x which becomes:
2x + (8/3)*x which becomes:
(14/3)*x
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the original cost to Michelle was:"
8x + 2y
since y = (2/3)*x then this cost becomes:
8x + (2*(2/3)*x which becomes:
8x + (4/3)*x which becomes:
(28/3)*x
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since michelle paid twice as much as martin, and:
(28/3)*x is 2 times (14/3)*x, then the equation looks good and you can say with reasonable confidence that the price of 9 oranges is 6 apples.
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