Question

Twice the greater of two consecutive odd integers is 13 less than three times the lesser, how do you find the integers?

Answer 1

The integers are `17` and `19`.

Explanation:

The trick when dealing with consecutive numbers of any kind is to use the smallest one to express the others.

In your case, if `x` is an odd number, the consecutive odd number will be `(x+2)`, since `(x+1)` would be an even number.

So, you know that if you double the bigger of the two numbers and add `13` to the result, you get a number that's three times larger than the smaller of the two numbers.

This is equivalent to saying that

`2 * underbrace((x+2))_(color(blue)("bigger number")) + 13 = 3 * underbrace(x)_(color(green)("smaller number"))`

This means that you have

`2(x+2) + 13 = 3x`

`2x + 4 + 13 = 3x => x = color(green)(17)`

The bigger number will be

`x+2 = 17 + 2 = color(green)(19)`