Let's define some variables first. I'm going to say that x = larger number and y = smaller number. Now let's set up our 2 equations (since we have 2 unknown variables, we need 2 equations to solve for them):
[tex]x+y=53[/tex]
[tex]3y=19+x[/tex]
Now, let's solve for x in the first equation, then plug it into the other one to get a tangible value for y:
[tex]x = 53-y[/tex]
[tex]3y=19+(53-y)[/tex]
[tex]3y = 72-y[/tex]
[tex]4y = 72[/tex]
[tex]y = \frac{72}{4} = 18[/tex]
Now that we know that y = 18, let's plug it back into the first equation to solve for x:
[tex]x + 18 = 53[/tex]
[tex]x = 53-18=35[/tex]
So, x = 35 and y = 18. Therefore, the larger number is equal to 35, and the smaller number is 18
