Fred is 10 yrs older than Ted. In 3 yrs time Fred will be 3 times as old as Ted.
Let Fred be x yrs old now.
Write an equation to represent this situation. Solve equation and state how old each person is now.
F = T + 10
F + 3 = 3(T+3)
T + 10 + 3 = 3 T + 9
2 T = 4
T = 2
F = 12
To represent this situation, we need to set up an equation based on the given information. Let's start by using the information that Fred is currently 10 years older than Ted, which means Fred's age is Ted's age plus 10:
Fred's age: x
Ted's age: x - 10
Moving on to the second piece of information, in 3 years' time, Fred will be 3 times as old as Ted. This means that Fred's age in 3 years will be equal to three times Ted's age in 3 years. Let's express this mathematically:
Fred's age in 3 years: x + 3
Ted's age in 3 years: (x - 10) + 3
Now we can write the equation based on the second piece of information:
x + 3 = 3((x - 10) + 3)
To solve this equation, we'll start by distributing 3 to the parentheses:
x + 3 = 3(x - 7)
Next, simplify by multiplying 3 to each term inside the parentheses:
x + 3 = 3x - 21
Now move all terms containing x to one side to isolate it:
x - 3x = -21 - 3
Simplifying further:
-2x = -24
Divide both sides by -2 to solve for x:
(-2x)/-2 = (-24)/-2
This gives us:
x = 12
Therefore, Fred is currently 12 years old and Ted is 2 years younger, so Ted is currently 2 years old.