The difference between the ages of two of my three grandchildren is 3. my eldestgrandchild is three times older than the age of my youngest grandchild and my eldest grandchild's age is two years more than the ages of my two youngest grandchildren added together. how old is my eldest grandchild?

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.