Question 396298: the product of two numbers is 96 their difference is 10 .what are the numbers Found 2 solutions by ewatrrr, Alan3354:Answer by ewatrrr(24785) (Show Source):
Hi
difference is 10
Let x and (x-10) represent the numbers
question states***
x(x-10) = 96
solving for x
x^2 - 10x = 96
x^2 - 10x - 96 = 0
(x - 16)(x + 6) = 0 Note:SUM of the inner product(-6x) and the outer product(6x) = -10x
(x - 16)=0
x = 16 this pair of Numbers are 16 and 6 | 6*16 = 96
(x + 6) = 0
x = -6 this pair Numbers are -6 and -16 | -1*-16 = 96
You can put this solution on YOUR website! Since the difference is 10, the units digits have to be the same.
Only 4*4 and 6*6 give a units digit in the product of 6.
4*24 is not it, and 14 is not a factor.
That leaves 6 & 16.
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You can work it out with algebra, but it takes longer.
If it's a question on a test, and showing work is not required, do it the fastest way possible.
