Ruffy is 34 as old as Orlie. Four years ago, Ruffy was 1 year more than 12 as old as Orlie. How old is each?
To solve this problem, we can assign variables to represent Ruffy's age and Orlie's age. Let's use the variable "R" for Ruffy and "O" for Orlie.
From the given information, we know that Ruffy is currently 34 years old, and that Ruffy's age is 34 years more than Orlie's age. So we can write the equation R = O + 34.
We are also told that four years ago, Ruffy was 1 year more than 12 times Orlie's age. This can be expressed as R - 4 = 12(O - 4) + 1.
Now we have two equations:
1) R = O + 34
2) R - 4 = 12(O - 4) + 1
We can solve this system of equations to find the values of R and O.
Let's substitute the value of R from equation 1 into equation 2:
(O + 34) - 4 = 12(O - 4) + 1
O + 30 = 12O - 48 + 1
O + 30 = 12O - 47
Next, let's simplify the equation:
O - 12O = -47 - 30
-11O = -77
Now, divide both sides of the equation by -11 to solve for O:
O = (-77) / (-11)
O = 7
We have found that Orlie is 7 years old.
Now, let's substitute this value back into equation 1 to find Ruffy's age:
R = O + 34
R = 7 + 34
R = 41
Therefore, Ruffy is 41 years old and Orlie is 7 years old.