Question

The sum of two numbers is
49
. The smaller number is
19
less than the larger number. What are the numbers

Answer 1

Call the two numbers "$a$" and "$b$". From the problem statement we know that "the sum of the two numbers is 49". So let's write that:

$a + b =49$

We also know that "the smaller number is 19 less that the larger number". Let's say that "$a$" is the larger number. We can then write:

$b = a -19$

We now have, 2 equations and 2 unknown numbers. We can solve by substitution.

We already have a substitution for "$b$" from our second equation, so let's drop that into the other one like so:

$a + b = 49$
$a + (a-19)=49$
$2a-19=49$
$2a=68$
$a=34$

There's our first answer.  $a=34$

We can then use our equation for "$b$":

$b = a - 19$
$b = 34 - 19$
$b = 15$


There's our second answer.  $b=15$

So: 
There's our answer.  $a=34 ; b=15$

Wwe can use our first equation to check our work:
$a+b=49$
$34+15=49$
$49=49$ CHECKS