Let the numbers be A and B.
Now their sum is A + B = 27
Their product is A*B = 140
A + B = 27
=> A = 27 - B
Substitute this in A*B = 140
=> (27 - B)*B = 140
=> 27B - B^2 = 140
=> B^2 - 27B + 140 = 0
=> B^2 - 20B - 7B + 140 =0
=> B( B - 20) - 7(B - 20) =0
=> (B - 7)(B - 20) = 0
So B is 7 and 20.
As A = 27 - B, A can be 20 and 7.
So, the two numbers are 20 and 7
Let us assume that the numbers are x and y.
Given the sum of the numbers is 27.
Then we will write:
x + y = 27 .............(1)
Also, given the sum of the numbers is 140.
==> x*y = 140 ............(2)
Now we will solve using the substitution method.
From (1) we know that: x = 27-y
==> x*y = 140
==> ( 27-y) *y = 140
==> 27y - y^2 = 140
==> y^2 - 27y + 140 = 0
==> ( y-20) ( y-7) = 0
==> y1 = 20 ==> x1= 7
==> y2 = 7 ==> x2= 20
Then, the numbers are 20 and 7.