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 years time .how old is peter now?
Let M and P be their ages now.
M = (2/3) P
M - 2 = (P+5) /2
Now, rearrange the last equation.
2M - 4 = P + 5
2M - P = 9
4M - 2P = 18
From the first equation,
3M - 2P = 0
Subtract the last equation from the one before it.
M = 18
P = 27
To find Peter's current age, let's represent it as 'P'.
According to the given information:
- Mary's age is 2/3 of Peter's age, which means Mary's age is (2/3)P.
- Two years ago, Mary's age was 1/2 of what Peter's age will be in 5 years. Let's break this down:
- Two years ago, Mary's age was (2/3)P - 2.
- In 5 years, Peter's age will be P + 5.
- So, according to the given information, (2/3)P - 2 = (1/2)(P + 5).
Now, let's solve the equation to find Peter's age (P):
(2/3)P - 2 = (1/2)(P + 5)
Multiply through by 6 to get rid of the fractions:
4P - 12 = 3(P + 5)
Distribute on both sides:
4P - 12 = 3P + 15
Combine like terms:
4P - 3P = 15 + 12
P = 27
Therefore, Peter is currently 27 years old.