Terry is 25 years older than Ron. in 5 years, he will be twice as old as Ron. Find their present ages.
Structured method:
Let Ron's age be x
Terry is x+25
in 5 years:
Ron's age = x+5
Terry's age = x+30
x+30 = 2(x+5)
x+30 = 2x+10
20 = x
Ron is now 20 and Terry is 45 years old
T=25+R
R=25-5=20
20+25=45
T=45
R=20
Let's solve the problem step by step:
Step 1: Assign variables:
Let's assign T for Terry's present age and R for Ron's present age.
Step 2: Formulate equations:
According to the given information:
Terry is 25 years older than Ron, which can be expressed as T = R + 25.
In 5 years, Terry will be twice as old as Ron, which can be expressed as T + 5 = 2(R + 5).
Step 3: Solve the equations:
Substitute the value of T from equation 1 into equation 2:
(R + 25) + 5 = 2(R + 5)
R + 30 = 2R + 10
R - 2R = 10 - 30
-R = -20
R = 20
Substitute the value of R into equation 1 to find Terry's age:
T = R + 25
T = 20 + 25
T = 45
Step 4: Final Answer:
Therefore, Terry's present age is 45 years, and Ron's present age is 20 years.
To solve this problem, we can set up two equations based on the given information.
Let's assume Ron's current age is R.
According to the problem, Terry is 25 years older than Ron, so Terry's current age is R + 25.
In 5 years, Ron's age will be R + 5, and Terry's age will be (R + 25) + 5.
The problem also states that in 5 years, Terry will be twice as old as Ron. So we can write the equation:
(R + 25) + 5 = 2(R + 5)
Now we can solve this equation to find Ron's current age.
R + 25 + 5 = 2R + 10
Simplifying the equation, we get:
R + 30 = 2R + 10
Subtracting R from both sides, we get:
30 = R + 10
Subtracting 10 from both sides, we get:
20 = R
So Ron's current age is 20 years old.
To find Terry's current age, we substitute Ron's age into Terry's age equation:
Terry's age = R + 25 = 20 + 25 = 45
Therefore, Ron's present age is 20 years, and Terry's present age is 45 years.