Find two numbers whose sum is 26 and whose product is 165.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let the two numbers be x and y. Their sum is 26 and the product is 165

sum = x + y = 26

=> x = 26 - y

product = x*y = 165

substitute x = 26 - y

=> (26 - y)*y = 165

=> 26y - y^2 = 165

=> y^2 - 26y + 165 = 0

=> y^2 - 15y - 11y + 165 = 0

=> y(y - 15) - 11(y - 15) = 0

=> (y - 15)(y - 11) = 0

y = 11 and y = 15

x = 26 - y = 15  and 11

The two numbers are 15 and 11.

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Let us assume that the numbers are x and y.

Given that the sum of the numbers is 26.

==> x+ y= 26............(1)

Also, given that the product is 165.

==> x*y = 165..........(2)

We will use the substitution method to solve for x and y.

From (1), we know that x= 26-y

Now we will substitute into (2).

==> (26-y)*y = 165

==> 26y - y^2 = 165

==> y^2 - 26y + 165 = 0

Now we will factor.

==> ( x-15)(x-11) = 0

==> x1= 15 ==> y1= 26-15 = 11

==> x2= 11 ==> y2= 26-11 = 15

Then, the numbers are 11 and 15.

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