The ages of three siblings combined is 27. The oldest is twice the age of the youngest. The middle child is 3 years older than the youngest. Write and solve an equation to find the ages of each sibling.
The youngest is X yrs. old.
Middle child is x+3 yrs. old.
The oldest is 2x yrs. old.
x + x+3 + 2x = 27.
X = ?
x+3 = ?
2x = ?
Let's set up the equations to solve this problem.
Let X be the age of the youngest sibling.
The oldest sibling is twice the age of the youngest, so the oldest sibling's age is 2X.
The middle sibling is 3 years older than the youngest, so the middle sibling's age is X + 3.
The sum of their ages is 27, so we have the equation:
X + 2X + (X + 3) = 27
Simplifying this equation:
4X + 3 = 27
Subtracting 3 from both sides:
4X = 24
Dividing both sides by 4:
X = 6
Therefore, the youngest sibling is 6 years old.
The oldest sibling is twice that age, so the oldest sibling is 12 years old.
The middle sibling is 3 years older than the youngest, so the middle sibling is 6 + 3 = 9 years old.
To summarize, the ages of the three siblings are as follows:
Youngest sibling: 6 years old
Middle sibling: 9 years old
Oldest sibling: 12 years old.
To solve this problem, let's use algebraic equations to represent the ages of the siblings.
Let's assign variables to each sibling's age:
- Let x be the age of the youngest sibling.
- Since the oldest sibling is twice the age of the youngest, the oldest sibling's age would be 2x.
- The middle child is 3 years older than the youngest, so the middle child's age would be x + 3.
Now, let's set up an equation for the given information: "The ages of three siblings combined is 27."
This can be represented as: x + 2x + (x + 3) = 27
Let's solve the equation:
Combining like terms, we get:
4x + 3 = 27
Subtracting 3 from both sides of the equation, we have:
4x = 24
Dividing both sides of the equation by 4, we get:
x = 6
Therefore, the youngest sibling is 6 years old.
To find the ages of the other siblings, substitute x back into our variables:
- The oldest sibling would be 2x = 2(6) = 12 years old.
- The middle child would be x + 3 = 6 + 3 = 9 years old.
So, the ages of the three siblings are:
- The youngest is 6 years old.
- The middle child is 9 years old.
- The oldest is 12 years old.