### Question:

Grandmother’s inheritance plan is filled with intriguing twists. Upon her passing, she divided her money, leaving half to her granddaughter and half of that amount to her grandson. A generous sixth of her wealth was bequeathed to her brother, and the remaining balance of $1,000 was devoted to supporting the animal shelter. What was the total amount of her inheritance?

### Answer:

**The total amount of Grandmother’s inheritance was $12,000.**

### Explanation

In this captivating financial puzzle, let’s navigate the path of Grandmother’s bequests and uncover the sum of her inheritance.

Step 1: Identify the Division of Wealth

- Half of Grandmother’s money was left to her granddaughter.
- Half of the amount given to the granddaughter was left to her grandson.
- A generous sixth of her wealth was given to her brother.
- The remaining balance of $1,000 was dedicated to the animal shelter.

Step 2: Expressing the Inheritance Mathematically Let’s use algebraic expressions to represent the different portions of Grandmother’s inheritance:

- Let “x” be the total amount of Grandmother’s money.

The division of wealth is as follows:

- Granddaughter’s share: 1/2 * x
- Grandson’s share: 1/2 * (1/2 * x) = 1/4 * x
- Brother’s share: 1/6 * x
- Animal shelter’s share: $1,000

Step 3: Formulate the Equation The sum of all these portions must add up to the total amount of Grandmother’s inheritance:

Equation: Granddaughter’s share + Grandson’s share + Brother’s share + Animal shelter’s share = Total inheritance (1/2 * x) + (1/4 * x) + (1/6 * x) + $1,000 = x

Step 4: Solve for “x” To find the total amount of Grandmother’s inheritance, we’ll solve the equation for “x”:

Multiplying all terms by the least common multiple (LCM) of 2, 4, and 6 (which is 12) to eliminate the fractions: (6x) + (3x) + (2x) + 12,000 = 12x

Combining like terms: 11x + 12,000 = 12x

Subtracting 11x from both sides of the equation:

12,000 = 12x – 11x

12,000 = x

Step 5: Final Answer Grandmother left a total amount of $12,000 as her inheritance. Through her thoughtful allocations, her legacy lives on, benefiting her loved ones and the noble cause of supporting the animal shelter. Your sharp financial acumen has successfully solved the puzzle, revealing the grand total of her inheritanceâ€”$12,000.