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?
M-5=2R+5
1/3(R+3)=(M+3)+12
Can you take it from here?
No - that comes out to a negative number - doesnt it? Can you show the next steps?? I am not sure why it is not coming out -
To solve this problem, we need to create a system of equations based on the given information.
Let's assume that Monty is currently M years old, and Rachel is currently R years old.
According to the first statement, "5 yrs ago Monty's age was 5 years less than twice Rachel's age," we can write the equation:
(M - 5) = 2(R - 5) - 5. Simplifying this equation, we get M - 5 = 2R - 15 - 5, which becomes M - 5 = 2R - 20.
Next, we consider the second statement: "In 3 years, one third of Rachel's age will be 12 years less than Monty's age." This gives us the equation:
((R + 3)/3) = (M + 3) - 12. Simplifying this equation, we get (R + 3)/3 = M - 9.
Now, we have a system of equations:
M - 5 = 2R - 20 ----(1)
(R + 3)/3 = M - 9 ----(2)
To solve this system, we will use the substitution method:
From equation (2), we can isolate M by multiplying both sides by 3:
R + 3 = 3(M - 9)
R + 3 = 3M - 27
R = 3M - 30 ----(3)
Now, substitute this value of R in equation (1):
M - 5 = 2(3M - 30) - 20
M - 5 = 6M - 60 - 20
M - 5 = 6M - 80
75 = 5M
M = 15
Now, substitute this value of M into equation (3) to find R:
R = 3M - 30 = 3(15) - 30 = 45 - 30 = 15
So, Monty is currently 15 years old, and Rachel is currently 15 years old as well.