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.
y = youngest , m = middle , e = eldest
y + m + e = 27
e = 2 y
m = y + 3
substituting ... y + y + 3 + 2 y = 27
To find the ages of each sibling, let's assign variables to their ages. Let's say the youngest sibling's age is "x", the middle sibling's age is "y", and the oldest sibling's age is "z".
From the information given, we can form three equations:
1) The ages of three siblings combined is 27:
x + y + z = 27
2) The oldest sibling is twice the age of the youngest:
z = 2x
3) The middle child is 3 years older than the youngest:
y = x + 3
Now, we have a system of three equations. We can solve this system by substituting equations (2) and (3) into equation (1).
Substituting z = 2x and y = x + 3 into x + y + z = 27, we get:
x + (x + 3) + 2x = 27
4x + 3 = 27
4x = 27 - 3
4x = 24
x = 24/4
x = 6
Now that we know the value of x (the age of the youngest sibling), we can substitute back into equations (2) and (3) to find y and z.
From equation (2):
z = 2x
z = 2(6)
z = 12
From equation (3):
y = x + 3
y = 6 + 3
y = 9
So, the youngest sibling is 6 years old, the middle sibling is 9 years old, and the oldest sibling is 12 years old.