One number is 7 less than another. The product of the numbers is 44. Find the numbers.

Question

campbell_st · Answer

well let x be one number, so the other number is x - 7

so 

x(x-7) = 44

which is 

$$x^2 - 7x - 44 = 0$$

just solve the quadratic for the solutions

anonymous · Answer

x(x-7)=44
x^2-7x-44=0
(x-11)(x+4)=0
I got X=11, -4 but my teacher said there was 4 answers

campbell_st · Answer

well thats not strictly correct as the 2nd number is dependent on the 1st... so there are 2 unique 1st numbers.... and the 2nd number depends on the 1st. 

the other method

let x be the smaller number... so the larger number is x + 7

so 

x(x + 7) = 44

or 

$$x^2 + 7x - 44 = 0$$

anonymous · Answer

Would they be (11,4) and (-4,11)?

campbell_st · Answer

so the solutions are

11 and 4 

-4 and - 11

anonymous · Answer

Gratzi!

anonymous · Answer

Would there always be 2 solutions to this type of problem or just depending on the numbers?

campbell_st · Answer

well a quadratic always has 2 solutions... they may be equal... as in a perfect square... or complex... or real... 

but always 2

anonymous · Answer

mkay, thanks.