SOLUTION: the ratio of the sum of 2 positive integers to their difference is 7:5. If the sum of the 2 number is at most 25, find all possible values for the pair of numbers

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Question 537080: the ratio of the sum of 2 positive integers to their difference is 7:5. If the sum of the 2 number is at most 25, find all possible values for the pair of numbers
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the ratio of the sum of 2 positive integers to their difference is 7:5. If the sum of the 2 number is at most 25, find all possible values for the pair of numbers
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Equations:
(x+y)/(x-y) = 7/5
x + y <=25
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Solve the equality:
5x+5y=7x-7y
12y = 2x
y = x/6
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%2F6%29
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And:
x+y = 25
(25)/(x-y) = 7/5
125 = 7x-7y
y = x-(125/7)
graph%28400%2C400%2C-10%2C10%2C-30%2C30%2Cx-%28125%2F7%29%29
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x-y = (125/7)
x+y = 25
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Add and solve for "x":
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2x = 300/7
x = 150/7
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Solve for "y":
x+y = 25
y = 25-(150/7)
y = 25/7
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Equality solution: (150/7 , 25/7)
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Inequality solution:
Since x+y <= 25
y <= 25-(150/7) <= 25/7
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Cheers,
Stan H.
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