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
