Question

Help me set this up...
The product of two consecutive positive integers is 5 more than their sum.

Find the integers:
Let x= 1st integer
Let x+5 = 2nd integer

What next? Stuck

Answer 1

Since it says product of two CONSECUTIVE positive integers,
Let x = 1st integer
x + 1 = 2nd integer
Let y be the sum of the two integers
So the product of the integers is 5 more than the sum
So (x)(x+1) = y +5,
Can you take it from here?

Answer 2

ok, let me see

Answer 3

(x)(x+1)=y+5
x^2+x=y+5
y=x^2+x-5

Ummm, guess not. Stuck again

Answer 4

You also have another equation, the sum of the two integers

Answer 5

\[x(x+1)=5+(x+(x+1))\] then \[x^{2}+x=2x+6\] so \[x^{2}-x-6=0\] so \[(x-3)(x+2)=0\]

Answer 6

but the number must be positive so the answer for x is 3 and x+1=4

Answer 7

Ok, that makes sense. I understand it this way Teresita.
Thanks, xNiker, I got confused with the y

Answer 8

Your welcome :), sorry for m grammar, I don't speak english

Answer 9

That's fine.

Answer 10

Eh, you could've just went
y + 5 = x(x+1), y = x^2 +x - 5
y= x + x + 1
Equate the two
2x + 1 = x^2 + x -5
x^2 - x - 6 = 0, then solve