The sum of two numbers is 27 and the product is 140 . What are the numebrs?
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
hala718 | High School Teacher | (Level 1) Educator Emeritus
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.
neela | High School Teacher | (Level 3) Valedictorian
Let the two numbers be x and 27-x as their sum is 27.
Since their product is 140, x(27-x) = 140.
27x-x^2 = 140.
=> x^2 -27x+ 140 = 0.
=> x^2- 20x-7x +140 = 0.
=> x(x-20) -7(x-20) = 0.
=> (x-20)(x-7) = 0.
=> x-20 = 0, or x-7 = 0.
=> x= 20, or x= 7.
Therefore x= 20, or x= 7.