Loretta's age now is twice John's age five years ago. In three years the sum of John's and Loretta's ages will be 50. How old are Loretta and John today?
John's present age ---- x
John's age 5 yrs ago = x-5
Loretta's present age = 2(x-5)
in 3 yrs from now:
John = x+3
Loretta = 2(x-5) + 3
x+3 + 2(x-5)+3 = 50
x+3 + 2x - 10 + 3 = 50
3x = 54
x = 18
NOW:
john = x = 18 yrs
Loretta = 2(x-5) = 26 yrs
check:
5 years ago, John was 13, which is twice Loretta's present age. Checks out!
in 3 yrs from now:
john + loretta = 21 + 29 = 50, all is good!
To solve this problem, we can set up a system of equations based on the given information.
Let's assume Loretta's age now as L and John's age now as J.
According to the first statement, Loretta's age now is twice John's age five years ago:
L = 2(J - 5) ---(Equation 1)
According to the second statement, in three years, the sum of John's and Loretta's ages will be 50:
(J + 3) + (L + 3) = 50 ---(Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) with two variables (L and J). We can solve this system to find the values of Loretta's and John's ages.
Let's solve Equation 1 first:
L = 2(J - 5)
L = 2J - 10
Now, substitute this expression for L in Equation 2:
(J + 3) + (2J - 10 + 3) = 50
J + 3 + 2J - 7 = 50
3J - 4 = 50
3J = 54
J = 18
Now that we know John's age (J = 18), we can substitute it back into Equation 1 to find Loretta's age:
L = 2(18 - 5)
L = 2(13)
L = 26
Therefore, Loretta is 26 years old and John is 18 years old today.