SOLUTION: the product of two number is between 40 and 60. one number is 10 less than the other. what are the two numbers?

Question 881338: the product of two number is between 40 and 60. one number is 10 less than the other. what are the two numbers?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let x be one number, then the other number is (x-10), we are given
40 < x*(x-10) < 60
40 < x^2 - 10x < 60
subtract 40 from all terms
0 < x^2 -10x -40 < 60
use quadratic formula to solve for x
x = (10 + square root(100-4(-40)) / 2 = 26.124515497/2 = 13.062257749
x = (10 - square root(100-4(-40)) / 2 = -16.124515497/2 = -8.062257749
we select 13.062257749 since it is > 0
our two numbers are 13.062257749, 3.062257749
note that 13.062257749 * 3.062257749 = 40.000000011 which is 40 < 40.000000011 < 60
our answer checks

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