Tina is 3 years younger than Tom. The ages are in the ratio 2:3. Find their ages.
tina/tom=2/3 or 2Tina=2Tom or Tina = 2tom/3
but
tina=tom-3 or
2Tom/3=tom-3
2om=3tom-9
tom=9
tima=6
Responses
To find the ages of Tina and Tom, we can start by setting up a system of equations based on the given information.
Let's assume that Tom's age is represented by x. Since Tina is 3 years younger than Tom, Tina's age can be represented as (x - 3).
We are also given that the ages are in the ratio 2:3. This means that the ratio of Tina's age to Tom's age is (x - 3) / x.
According to the given ratio, we can set up the following equation:
(x - 3) / x = 2 / 3
To solve this equation, we can cross multiply:
3(x - 3) = 2x
3x - 9 = 2x
Next, we can subtract 2x from both sides to isolate the x term:
3x - 2x - 9 = 2x - 2x
x - 9 = 0
Now, add 9 to both sides of the equation to solve for x:
x - 9 + 9 = 0 + 9
x = 9
Therefore, Tom's age is 9 years old.
Now that we know Tom's age, we can find Tina's age by substituting the value of x into the equation (x - 3):
Tina's age = 9 - 3 = 6
Thus, Tina is 6 years old and Tom is 9 years old.