SOLUTION: One number is 1 more than 2 times another. Their product is 10. Find the numbers.

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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):
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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