Integer word problems

Question

An integer is 9 more than 2 times another. If the product of the two integers -10, then find the integers. 

Answer 1

Hello Amber,

Let x and y be the two integers.

 

From the first sentence, we get:

y = 2x + 9 {Equation 1}

 

From the second sentence:

xy = -10 {Equation 2}

 

Plugging {Equation 1} into {Equation 2} yields:

x(2x + 9) = -10

→ 2x² + 9x = -10

→ 2x² + 9x +10 = 0

 

To factor a quadratic, ax² + bx + c,  where 'a' does not equal 1, multiply 'a' and 'c' together to get 20.

4 times 5 equals 20, and 4 plus 5 add to 9.

So let's break the middle term up to get:

2x² + 4x + 5x +10 = 0.  Now factor by grouping:

→ 2x(x + 2) + 5(x + 2) = 0. Factor out the (x+2):

→ (x + 2)(2x + 5) = 0

 

So either x + 2 = 0 or 2x + 5 = 0

→ x = -2 or x = -5/2.

 

Since -5/2 is not an integer,

x = -2

→ y = 5

 

Hope the above helps, and thank you for posting the question.

Michael Ehlers