Let
x = the age of the youngest grandchild
y = the age of the middle grandchild
z = the age of the oldest grandchild
"my eldest grandchild is three times older than the age of my youngest grandchild"
z = 3x
"my eldest grandchild's age is two years more than the ages of my two youngest grandchildren added together"
z = x + y + 2
"The difference between the ages of two of my three grandchildren is 3."
We are not told which of the three grandchildren are 3 years apart.It may be x and y, or y and z, or x and z.
Let's try x and y.
z = 3x
z = x + y + 2
y = x + 3
z = 3xz = x + x + 3 + 2
z = 2x + 5
3x = 2x + 5
x = 5
y = x + 3 = 5 + 3 = 8
z = 3x = 3 * 5 = 15
Answer: The eldest grandchild is 15 years old.
