David is three years older than John.In 8years time, John age will be 7/8 of David's age.find their age.
John's age --- x
David's present age --- x+3
in 8 yrs:
John = x+8
David = x+3 + 8 = x+11
x+8 = (7/8)(x+11)
solve for x and finish
Thank you reiny
To solve this problem, we can set up equations based on the given information. Let's suppose John's age is J years old, and David's age is D years old.
Given that David is three years older than John, we can write the equation:
D = J + 3 -- (Equation 1)
In eight years, John's age will be J + 8 years old, and David's age will be D + 8 years old.
Given that John's age in 8 years will be 7/8 of David's age, we can write the equation:
J + 8 = (7/8)(D + 8) -- (Equation 2)
Now, we have a system of two equations (Equation 1 and Equation 2) and two variables (J and D). Let's solve this system:
Step 1: Substitute the value of D from Equation 1 into Equation 2:
J + 8 = (7/8)(J + 3 + 8)
Step 2: Simplify the equation:
J + 8 = (7/8)(J + 11)
Multiply both sides by 8 to eliminate the fraction:
8(J + 8) = 7(J + 11)
8J + 64 = 7J + 77
8J - 7J = 77 - 64
J = 13
Step 3: Substitute the value of J into Equation 1 to find D:
D = J + 3
D = 13 + 3
D = 16
Therefore, John is 13 years old, and David is 16 years old.