Question

Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?

Answer 1

i guess but i stilll no understand

Answer 2

Ok one integer is represented by x. The consecutive integer would be x+1. do you understand that?

Answer 3

yes

Answer 4

Ok so if x is the first and x+1 is the second, then 2x+2 is twice the second right?

Answer 5

right and did you factor out a 2?

Answer 6

well not yet...

Answer 7

So the question reads that the first integer multiplied by 2 times the second will be 612. So x * (2x+2) = 612

Follow so far?

Answer 8

im with you on this

Answer 9

Great! So when you multiply out, you get

2x^2 + 2x = 612

Answer 10

Then you divide everything by 2:
x^2 + x = 306

Answer 11

ok

Answer 12

Then you solve for x by getting it to the form ax^2 + bx + c =0 and factoring

Answer 13

(x +18)(x - 17) = 0
x = -18, 17

But you need the two that are consecutive, and since there was a square, you can look for different signed answers. So the two integers are 17 and 18.

To check: 17 * (2*18) = 17 * 36 = 612

Answer 14

oh ok thanks now i understand it.

Answer 15

great!