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

Call the two numbers "[latex]a[/latex]" and "[latex]b[/latex]". From the problem statement we know that "the sum of the two numbers is 49". So let's write that: [latex] a + b =49 [/latex] We also know that "the smaller number is 19 less that the larger number". Let's say that "[latex]a[/latex]" is the larger number. We can then write: [latex] b = a -19 [/latex] We now have, 2 equations and 2 unknown numbers. We can solve by substitution. We already have a substitution for "[latex]b[/latex]" from our second equation, so let's drop that into the other one like so: [latex] a + b = 49 [/latex] [latex] a + (a-19)=49[/latex] [latex]2a-19=49[/latex] [latex]2a=68[/latex] [latex]a=34[/latex] There's our first answer. [latex]a=34[/latex] We can then use our equation for "[latex]b[/latex]": [latex]b = a - 19[/latex] [latex]b = 34 - 19[/latex] [latex]b = 15[/latex] There's our second answer. [latex]b=15[/latex] So: There's our answer. [latex]a=34 ; b=15[/latex] Wwe can use our first equation to check our work: [latex]a+b=49[/latex] [latex]34+15=49[/latex] [latex]49=49[/latex] CHECKS