Mr. Benedict left half of his estate to his wife, one-fourth to his son, one-fifth to his daughter and the remainder, $5000 to his college. What is the total amount left by Mr. Benedict?

a. $ 9,250
b. $ 10,000
c. $ 16,000
d. $ 50,000
e. $ 100,000

please answer and explain

0.5x + 0.25x + 0.2x + 5000 = x

0.95x + 5000 = x

5000 = 0.05x

100,000 = x

thank you, Ms. Sue

You're welcome, Thomas.

To find the total amount left by Mr. Benedict, we need to add up the fractions of his estate that he left to his wife, son, daughter, and college.

Let's start by calculating the fraction of his estate that Mr. Benedict left to his wife. He left half of his estate to his wife, so the fraction is 1/2.

Similarly, Mr. Benedict left one-fourth of his estate to his son, so the fraction is 1/4.

He also left one-fifth of his estate to his daughter, so the fraction is 1/5.

The rest, $5000, was left to his college.

To calculate the total amount left by Mr. Benedict, we can sum up these fractions:

1/2 + 1/4 + 1/5

To do this calculation, we need to find a common denominator for these fractions. The lowest common multiple of 2, 4, and 5 is 20.

So, we need to rewrite the fractions with a denominator of 20:

10/20 + 5/20 + 4/20
(10 + 5 + 4) / 20
19/20

Therefore, Mr. Benedict left 19/20 of his estate, or $5000, to his college. To find the total amount left by Mr. Benedict, we divide $5000 by the fraction 19/20:

Total amount left = $5000 ÷ (19/20)
Total amount left = $5000 × (20/19)
Total amount left = $5263.16 (rounded to the nearest cent)

Given the answer options, the closest amount to $5263.16 is $5250, which is option A: $9,250. Therefore, the correct answer is option A: $9,250.