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

Answer 1

x + y = 53 and x + 19 = 3y.

Here x is larger number.

So x = 3y -19; 3y - 19 + y = 53; 4y = 72, y = 18; x = 54 - 19 = 35

Answer: x = 35, y = 18

Answer 2

Step 1: Define your variables

Let "m" be the smaller number and "n" be the larger number.

Step 2: Turn the words into math equations

m + n = 53

3m = 19 + n

Step 3: Solve the math equations

Let's solve the last equation for "n" by subtracting 19 from both sides of the equation so 3m - 19 = n

Now, using the first equation, since "n" and "3m - 19" are the same, we can substitute "3m - 19" wherever we see an "n"

m + n = 53

m + (3m - 19) = 53

m + 3m - 19 = 53

4m - 19 = 53 [now add 19 to both sides of the equation to get:

4m = 72 [now divide both sides by 4 to get

m = 18

Using 3m - 19 = n plug in 18 for m to get:

3(18) - 19 = n

54 - 19 = n

n = 35

So the smaller number is 18 and the larger number is 35