SOLUTION: The product of 2 numbers is 91. The larger of the 2 numbers is one less than twice the smaller. Find the 2 numbers

Question 935400: The product of 2 numbers is 91. The larger of the 2 numbers is one less than twice the smaller. Find the 2 numbers
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = larger number
y = smaller number
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xy = 91
x = 2y - 1
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xy = 91
(2y - 1)y = 91
2yy - y - 91 = 0
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the above quadratic equation is in standard form, with a=2, b=-1 and c=-91
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 -1 -91
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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y = 7
y = -6.5
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the negative root doesn't fit the problem statement, so use the positive root:
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y = 7
x = 2y - 1
x = 2*7 - 1
x = 13
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or
y = -6.5
x = 2y - 1
x = 2*(-6.5) - 1
x = -14
in this case x is smaller than y, and if we reverse the roles of x and y, (x=-6.5 and y=-14), the numbers don't fit the problem statement (x = 2y - 1 is not true)
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answer:
x = 13
y = 7
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