mary's age is 2/3 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?
Peter's present age ---> x
Mary's present age ---> (2/3)x
Mary's age two yrs ago = (2/3)x - 2
Peter's age 5 yrs from now = x+5
"Two years ago mary's age was 1/2 of what peter's age will be in 5 years time." ---> (2/3)x - 2 = (1/2)(x + 5)
multiply by 6
4x - 12 = 3x + 15
x = 27
Peter is now 27 and Mary is now 18
check:
Mary's age 2 yrs ago = 16
Peter's age 5 yrs from now = 27+5 = 32
Is 16 one-half of 32 ??
Looks good
thx
To find Peter's age, we need to solve the problem using algebra. Let's assume Peter's current age is x.
Since Mary's age is 2/3 of Peter's, we can say her age is (2/3)x.
Two years ago, Mary's age was (2/3)x - 2, and Peter's age in 5 years will be x + 5.
According to the problem, Mary's age two years ago was 1/2 of what Peter's age will be in 5 years. So, we can write the equation:
(2/3)x - 2 = (1/2)(x + 5)
Now, let's solve for x:
Multiply both sides by 6 to eliminate the fractions:
6((2/3)x - 2) = 6(1/2)(x + 5)
4x - 12 = 3x + 15
Simplify the equation by combining like terms:
4x - 3x = 15 + 12
x = 27
Therefore, Peter is currently 27 years old.