# The sum of two numbers is 27 and the product is 140 . What are the numebrs?

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

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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.

Approved by eNotes Editorial Team