There are two numbers, which sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers

X + y = 53.

Let x be the smaller number; then it'll be 3x = 19 + y

Set the first equation equal to x, then substitute the values and solve.

x + y = 53.

x = 53 - y.

3 (53 - y) = 19 + y

x = 18; y = 35

140 - y = y

y = 70.

53 - 70 = - 17

x = - 17; y = 70.

-17 + 70 = 53;

Let "n" be the smaller number, then

the larger number = 3n-19

n + 3n - 19 = 53

4n = 53 + 19

4n = 72

n = 72/4

n = 18 ← smaller number

larger number = 53 - 18 = 35

Answer: 18 and 35.