Question 4084: Upon his death, Mr. Haller left one-half of his estate to his wife, one-ninth of his estate to each of his three children,
one-twenty-fourth of his estate to each of his three grandchildren, and the remaining $18,000 to his favorite charity.
What was the value of his estate?
Found 3 solutions by Earlsdon, WannabeCAgirl83, bonster:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let x = the inital value of the estate.
x - (1/2)x - (3/9)x - (3/24)x = $18,000 Find the common denominator and add the fractions.
x - (12/24)x - (8/24)x - (3/24)x = $18,000
x - (23/24)x = $18,000
(1/24)x = $18,000 Multiply both sides by 24.
x = $432,000
Answer by WannabeCAgirl83(35) (Show Source):
You can put this solution on YOUR website!
You have...
1/2
1/9 ∙ 3
1/24 ∙ 3
3 is nothing other than 3/1, so you have...
1/2
1/9 ∙ 3/1
1/24 ∙ 3/1
Step # 1
Multiplying the given fractions:
1/2
1/9 ∙ 3/1 = 3/9 (rule for multiplication: numerator ∙ numerator, denominator ∙ denominator)
1/24 ∙ 3/1 = 3/24
Step # 2
Finding a common denominator:
You need to add these fractions together later on. In order to add fractions together, all of them must have the same denominator. The least common denominator for those 3 fractions is 72...
1/2 ∙ 36/36 = 36/72
3/9 ∙ 8/8 = 24/72
3/24 ∙ 3/3 = 9/72
Step # 3
Adding fractions together:
Now as all 3 fractions have the same denominator, you can add them together...
36/72 + 24/72 + 9/72 = 69/72 (rule for addition: numerator + numerator, denominator stays unchanged)
Step # 4
Finding the difference between 69/72 and “the whole” (72/72):
69/72 = the amount Mr. Haller gave to his wife, children and grand children
72/72 = the whole amount his estate is worth
the difference between 69/72 and 72/72 = the remaining $ 18,000 he gave to his favorite charity
In order to find the difference you subtract 69/72 from 72/72...
72/72 – 69/72 = 3/72 (rule for subtraction: numerator – numerator, denominator stays unchanged)
3/72 = the remaining $ 18,000 he gave to his favorite charity
Step # 5
Dividing 69 (from 69/72) by 3 (from 3/72):
69 : 3 = 23
Step # 6
Multiplying 18,000 by 23 in order to find the amount of “the whole” (72/72):
18,000 ∙ 23 = 414,000
Answer: The value of his estate was $ 414,000. (72/72 = 414,000)
Answer by bonster(299) (Show Source):
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