Final answer:
The correct equation to represent the situation is 2x + x + (x + 4) + 3(x + 4) = 72. By defining 'x' as Jiro's age and expressing the other ages in terms of 'x', we find that Jiro is 8 years old, which allows us to calculate everyone's age.
Step-by-step explanation:
To solve the age problem, we need to use algebra to create an equation that represents the situation. We know that Alita is 2 times as old as Jiro, Jiro is 4 years younger than Erik, Erik is 1/3 as old as Dawn, and the sum of all their ages is 72 years. Let's denote the ages of Alita, Jiro, Erik, and Dawn with the variables A, J, E, and D respectively.
From the given information we can say:
- A = 2J (Alita is 2 times as old as Jiro)
- J = E - 4 (Jiro is 4 years younger than Erik)
- E = D/3 (Erik is 1/3 as old as Dawn)
In terms of Jiro's age (let's use 'x' for Jiro's age), we can rewrite these equations as:
- A = 2x
- E = x + 4
- D = 3E = 3(x + 4)
The sum of their ages is 72, so we have the equation: 2x + x + (x + 4) + 3(x + 4) = 72.
This simplifies to: 2x + x + x + 4 + 3x + 12 = 72. Combining like terms results in: 7x + 16 = 72. Subtracting 16 from both sides gives us 7x = 56, and dividing both sides by 7 yields x = 8.
Therefore, Jiro is 8 years old, Alita is 16 years old (2 x 8), Erik is 12 years old (8 + 4), and Dawn is 36 years old (3 x (8 + 4)).