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.