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Question 1032781: One number is 1 more than 2 times another. Their product is 10. Find the numbers.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the first number be a.
let the second number be b.
a = 2b + 1
ab = 10
in the second equation, replace a with 2b + 1 to get:
(2b + 1) * b = 10
simplify to get 2b^2 + b = 10
subtract 10 from both sides of the equation to get 2b^2 + b - 10 = 0
factor the quadratic equation to get (b - 2) * (2b + 5) = 0
solve for b to get b = 2 or b = -5/2
since a = 2b + 1, you get a = 5 which b = 2, and you get a = -4 when b = -5/2.
when a = 5 and b = 2, ab = 10 becomes 5*2 = 10 which becomes 10 = 10.
when a = -4 and b = -5/2, you get ab = 10 becomes -4 * -2.5 = 10 which becomes 10 = 10.
the value look good.
your solutions are:
a = 5 when b = 2
a = -4 when b = -5/2
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