Eight years ago martha was half as old as susan will be when susan is one year older than rose will be at the time when martha will be five times as old as rose will be two year from now.
ten years from now rose will be twice as old as susan was when martha was nine times as old as rose.
when rose was 1year old,martha was 3years older than rose will be when susan is three time as old as martha was 6years before the time when susan was 1/3 as old as rose will be when martha will be 3times as old as she was when susan was born.
How old are they now?
plz show work plz!!!
That's just plain silly.
no it a question
To solve this problem, we need to break it down into smaller steps and work out the ages of each person systematically. Let's solve it step-by-step:
Step 1: Establishing Variables
Let's assign variables to each person's current age:
- Martha's current age = M
- Susan's current age = S
- Rose's current age = R
Step 2: Translating the Information into Equations
Using the information given in the problem, we can create equations to represent the relationships between the ages of the three individuals. Let's go through each condition one by one:
Condition 1: "Eight years ago, Martha was half as old as Susan will be when Susan is one year older than Rose will be at the time when Martha will be five times as old as Rose will be two years from now."
This can be written as:
M - 8 = (S + (R + 1)) / 2 (Equation 1)
Condition 2: "Ten years from now, Rose will be twice as old as Susan was when Martha was nine times as old as Rose."
This can be written as:
(R + 10) = 2 * (S - (M - 9)) (Equation 2)
Condition 3: "When Rose was 1 year old, Martha was 3 years older than Rose will be when Susan is three times as old as Martha was 6 years before the time when Susan was 1/3 as old as Rose will be when Martha will be 3 times as old as she was when Susan was born."
This can be written as:
(M - (S - 1 / 3 * (R + 6))) = (R + (S * 3) - (R + 1)) + 3 (Equation 3)
Step 3: Solving the Equations
Now that we have three equations, we can solve them to find the values of the unknowns (M, S, R). We will use a method called substitution to solve them.
Let's solve Equation 1 for M:
M = (S + (R + 1)) / 2 + 8
Now substitute this value of M in Equations 2 and 3 to find the values of S and R.
Substituting M in Equation 2:
(R + 10) = 2 * (S - ((S + (R + 1)) / 2 + 8 - 9))
Simplify Equation 2.
Substituting M in Equation 3:
((S + (R + 1)) / 2 + 8 - (S - 1 / 3 * (R + 6))) = (R + (S * 3) - (R + 1)) + 3
Again, simplify Equation 3.
Now you have a system of equations in terms of S and R, which you can solve using methods like substitution or elimination. Solve the system of equations to find the values of S and R. Once you have those, substitute them back into Equation 1 to find the value of M.
As a general reminder, be careful with the calculations and double-check your work to ensure accuracy.