peter is twice as old as paul was when peter was as old as paul is now. the combined ages of peter and paul is is 56 years. how old are peter and paul now?
Let's assume the current age of Peter is P years and the current age of Paul is Q years.
According to the given information:
1. Peter is twice as old as Paul was when Peter was as old as Paul is now.
This means that when Peter was Q years old, Paul was (Q - P) years old.
Since Peter is twice as old as Paul was at that time:
P = 2*(Q - P) ---> P = 2Q - 2P ---> 3P = 2Q .......(Equation 1)
2. The combined ages of Peter and Paul is 56 years:
P + Q = 56 .......(Equation 2)
Now, we can solve these two equations to find the ages of Peter and Paul.
From Equation 1, we can express Q in terms of P:
3P = 2Q ---> Q = (3P)/2
Substituting Q in Equation 2, we have:
P + (3P)/2 = 56
Multiplying through by 2 to get rid of the fraction:
2P + 3P = 112
5P = 112
P = 112 / 5
P ≈ 22.4
Substituting P back into Equation 2, we can find Q:
22.4 + Q = 56
Q = 56 - 22.4
Q = 33.6
Therefore, Peter is approximately 22.4 years old and Paul is approximately 33.6 years old now.
To solve this problem, we can use algebraic expressions to represent the ages of Peter and Paul. Let's assume that Peter's current age is P and Paul's current age is Q.
According to the problem, "Peter is twice as old as Paul was when Peter was as old as Paul is now." This means that when Peter was Q years old, Paul was Q/2 years old.
Now, let's find the difference in ages between Peter and Paul at that time: P - (Q/2).
According to the problem, "the combined ages of Peter and Paul is 56 years," so we can write the equation: P + Q = 56.
We can now set up another equation using the information from the first part: P - (Q/2) = Q.
To solve the system of equations, we can substitute the value of P in terms of Q from the second equation into the first equation.
P = Q + (Q/2)
Simplifying, we get: P = (3Q/2)
Substituting this value of P into the equation P + Q = 56, we have:
(3Q/2) + Q = 56
Multiplying through by 2 to get rid of the fraction, we have:
3Q + 2Q = 112
5Q = 112
Dividing both sides by 5, we find:
Q = 22.4
Since we're dealing with ages, we cannot have a fraction of a year, so we round down to the nearest whole number.
Q ≈ 22
Now substituting this value of Q back into the equation P + Q = 56, we can solve for P:
P + 22 = 56
P = 56 - 22
P = 34
Therefore, Peter is currently 34 years old and Paul is currently 22 years old.
Peter's age now: x
Paul's age now: y
x-y years ago, Peter was y years old.
x = 2(y-(x-y))
x+y = 56
Peter is 32
Paul is 24
8 years ago, Peter was 24 and Paul was 12.