The sum of two integers is 18. Their product is 80. Find the numbers.

Question

i need help on this math problem and if anyone could help me please

 

Answer 1

Let one integer = x

Let the other = y

 

Using these variables we can write a system of equations.

 

x + y = 18                 eq1

xy = 80                     eq2

 

 

If we substitute eq1 into eq2 so that we have only one equation with only variable, we obtain

 

x(18 - x) = 80

 

 

Distributing, we get

 

18x - x² = 80

 

 

Subtract 18 and add x² to both sides of the equation.

 

0 = x² - 18x + 80

 

 

We now have a quadratic equation.  Solve for x to obtain one of the integers.  Do you know how to solve a quadratic equation?

 

 

Answer 2

Hi Ramiro

 

Let X & Y be the two integers

 

X+Y=18      Y = 18-X

XY = 80

 

We can substitute 18-X for Y in the equation XY = 80

X(18-X) = 80

 

Distributing

18X - X² = 80

 

Subtract 80 from both sides so that the equation is equal to 0

 

-X² + 18X - 80 = 0

Multiply (or divide by -1 so that the leading coefficient is positive, not negative)

X² - 18X + 80 = 0

 

We can factor this quadratic

 

(X-10)(X-8) = 0

 

Setting each factor equal to 0 we can solve for X.

 

X-10 = 0       X-8 = 0

X = 10          X = 8

 

The two integers are 8 and 10.