How do you find two consecutive odd integers such that 2 times the lesser is 19 less than 3 times the greater?

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Answer 1 · 2016-10-21T09:14:28

The numbers are $13 and 15$

Consecutive odd numbers differ by 2.
If the smaller one is called $x$ , the larger one will be $x+2$

We will be working with 2 terms which differ by 19.

This can be written in 3 different ways. Use the form which makes the most sense to you. They are all correct.

$"smaller" +19 = "BIGGER"" "larr$ I will use this one

$"BIGGER - smaller" = 19$

$"BIGGER" - 19 = "smaller"$

$2x +19 = 3(x+2)$

$2x+19 = 3x +6" "larr$ move x terms to one side

$19-6 = 3x-2x$

$13 = x$

$x=13" "larr$ the first odd number.

The next odd number is $15$ .