Question

The sum of two numbers is 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

Answer 1

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):

`x+y=53`

`3y=19+x`

Now, let's solve for x in the first equation, then plug it into the other one to get a tangible value for y:

`x = 53-y`

`3y=19+(53-y)`

`3y = 72-y`

`4y = 72`

`y = (72)/(4) = 18`

Now that we know that y = 18, let's plug it back into the first equation to solve for x:

`x + 18 = 53`

`x = 53-18=35`

So, x = 35 and y = 18. Therefore, the larger number is equal to 35, and the smaller number is 18