5 yrs ago Montys age was 5 years less than twice Rachels age. In 3 years, one third of Rachels age will be 12 years less than Montys age. How old are they now?
To solve this problem, let's start by assigning variables. Let Monty's current age be represented by M, and Rachel's current age be represented by R.
From the given information, we can generate the following equations:
Equation 1: 5 years ago, Monty's age was 5 years less than twice Rachel's age. This can be written as:
M - 5 = 2(R - 5)
Equation 2: In 3 years, one third of Rachel's age will be 12 years less than Monty's age. This can be written as:
(M + 3) - 12 = (1/3)(R + 3)
Our goal is to solve for M and R.
To simplify Equation 1, we can expand and rearrange it:
M - 5 = 2R - 10
M = 2R - 10 + 5
M = 2R - 5
Next, let's simplify Equation 2:
M + 3 - 12 = (1/3)(R + 3)
M - 9 = (1/3)(R + 3)
3M - 27 = R + 3
3M = R + 3 + 27
3M = R + 30
R = 3M - 30
Now that we have two expressions for Monty's age in terms of Rachel's age, we can substitute Equation 1 into Equation 2 to eliminate M:
2R - 5 = 3R - 30
-5 + 30 = 3R - 2R
25 = R
Substituting this value back into Equation 1:
M = 2R - 5
M = 2(25) - 5
M = 50 - 5
M = 45
Therefore, Monty is currently 45 years old, and Rachel is currently 25 years old.