There are two numbers whose sum is 53. three times the smaller is equal to 19 more than the larger number. what are the numbers?

Two numbers whose sum is 53=X+Y

Transpose Y to the other side to obtain: X=53-Y - Equation 1

3X=19+Y - Equation 2

Substitute Equation 1 into Equation 2: 3 (53-Y) = 19+Y - use distributive property to distribute 3

159-3Y=19+Y group similar expressions by using transposition

140=4Y divide both sides by four

35=Y

53=X+35 transpose 35 to the left side

53-35=X

X=18

The numbers are 35 and 18