SOLUTION: The larger of two number is 5 more than the smaller.If their product is 84,what are the numbers?

Question 774959: The larger of two number is 5 more than the smaller.If their product is 84,what are the numbers?
Answer by pakhi(24) (Show Source): You can put this solution on YOUR website!
Let the numbers be 'x' and 'y'.
Let the larger number be 'x'.
So x = y + 5 -----------------(1)
Also xy = 84 -------------------(2)
Putting the value of 'x' from equation 1 in equation 2 we get
(y + 5)y = 84
or y^2 + 5y = 84
or y^2 + 5y - 84 = 0
or y^2 - 7y + 12y - 84 = 0
or y(y-7) + 12(y-7) = 0
or (y - 7)(y + 12) = 0
or y = 7 or -12
So x = y + 5 = 7 + 5 = 12
or
x = y + 5 = -12 + 5 = -7
Therefore the two numbers are either (12,7) or (-7,-12)
check: xy = 84
Putting the two sets of values in the above equation we have
i) 12*7 = 84
ii) (-7)*(-12) = 84

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