Mary's age is 2/3 that of peter's. Two years ago Mary's age was 1/2 of what Peter's age will be in 5 year's time. How old is peter now?
Let P=peter's age, and
M=Mary's age.
M=(2/3)P.... (1)
Two years ago, Mary's age was M-2, and it was what Peter's age will be in 5 years time (P+5)/2
Therefore
M-2 = (P+5)/2
Substitute M from (1)
(2/3)P-2 = (P+5)/2
Solve for P to get P=27, and M=18
To solve this problem, let's represent Mary's current age as M and Peter's current age as P.
According to the problem, Mary's age is 2/3 that of Peter's. So we can write the equation:
M = (2/3) * P
The problem also states that two years ago, Mary's age was 1/2 of what Peter's age will be in 5 years' time. This can be expressed as:
M - 2 = (1/2) * (P + 5)
Now we have a system of two equations. We can solve this system to find the values of M and P.
Let's solve the first equation for M in terms of P:
M = (2/3) * P
Now substitute M in the second equation with (2/3) * P:
(2/3) * P - 2 = (1/2) * (P + 5)
To avoid fractions, we can multiply both sides of the equation by 6 to eliminate denominators:
2P - 12 = 3(P + 5)
Simplify the equation:
2P - 12 = 3P + 15
Subtract 2P from both sides:
-12 = P + 15
Subtract 15 from both sides:
-27 = P
Therefore, Peter's age is -27 years. However, this doesn't make sense, as age cannot be negative. It seems there might be an error in the problem or the data provided.
Please double-check the information given or provide additional details so that I can assist you further.