when I multiply my first number by 3 and my second lucky number by 2, the addition of the resulting produces a sum of 93. when I add twice my first lucky number to my second lucky number the sum is 53. what are my lucky numbers?

Let f = first lucky number, and let s = second lucky number.

Translate the sentences into two equations in two unknowns, and solve the system of equations to find the two unknowns.

"when I multiply my first number by 3 and my second lucky number by 2, the addition of the resulting produces a sum of 93."

3f + 2s = 93

"when I add twice my first lucky number to my second lucky number the sum is 53."

2f + s = 53

Now you have a system of equations.

3f + 2s = 93

2f + s = 53

Let's use the substitution method. Solve the second equation for s.

s = 53 - 2f

Now we substitute 53 - 2f for s in the first equation.

3f + 2s = 93

3f + 2 (53 - 2f) = 93

Distribute the 2.

3f + 106 - 4f = 93

Combine like terms on the left side.

-f + 106 = 93

Subtract 106 from both sides.

-f = - 13

Divide both sides by - 1.

f = 13

Now substitute f = 13 in the second original equation.

2f + s = 53

2 (13) + s = 53

26 + s = 53

Subtract 26 from both sides.

f = 27

Answer: The first lucky number is 13, and the second lucky number is 27.