SOLUTION: Kelvin leaves his property to be devided between a wife,a son,and a daughter so that the wife's share to the son's share is in the ratio of 5 to 3, and the son's to daughter's in t

Question 1148550: Kelvin leaves his property to be devided between a wife,a son,and a daughter so that the wife's share to the son's share is in the ratio of 5 to 3, and the son's to daughter's in the ratio of 4 to 3.if the wife has 561,000 more than the daughter,what is the value of the property of Mr Kelvin?.
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p = value of kelvin's property.
w = his wife's share.
s = his son's share.
d = his daughter's share.

w/s = 5/3
s/d = 4/3
w = d + 561000
p = w + s + d

in s/d = 4/3, solve for s to get s = 4d/3.

in w/s = 5/3, replace s with (4d/3) to get w/(4d/3) = 5/3
cross multiply to get 3w = 4(4d/3)
simplify to get 3w = 16d/3
divide both sides of this equation by 3 to get:
w = 16d/9

in w = d + 561000, replace w with 16d/9 to get:
16d/9 = d + 561000
multiply both sides of this equation by 9 to get:
16d = 9d + 5049000
subtract 9d from both sides of this equation to get:
11d = 5049000
solve for d to get:
d = 5049000 / 11 = 459000

since w = d + 591000, solve for w to get w = 1020000

since s/d = 4/3, replace d with 459000 to get:
s/d = s/459000 = 4/3
cross multiply to get 3s = 4*459000
solve for s to get s = 4*459000/3 = 612000

you have:
w = 1020000
s = 612000
d = 459000
p = w + s + d = 1020000 + 612000 + 459000 = 2091000

that's your answer.
the value of kelvin's property is 2,091,000.
his wife's share is 1,020,000.
his son's share is 612,000
his daughter's share is 459,000

the ratio of his wife's share to his son's share is equal to 5/3 = 1.6666.....
1020000/612000 = 1.6666...
they're the same, so the ratio is correct.

the ratio of his son's share to his daughter's share is 4/3 = 1.3333.....
612000/459000 = 1.333....
the're the same, so the ratio is correct.

his wife's share is 561000 more than his daughter's share.
459000 + 561000 = 1020000, so that's also correct.

add up his wife's share and his son's share and his daughter's share and your solution is that the value of kelvin's property is 2,091,000, as stated above.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

wife:son = 5:3
son:daughter = 4:3

Change the ratios to equivalent ratios so that the son's share is the same number in both ratios:

wife:son = 20:12
son:daughter = 12:9

Now we can combine the ratios to compare all three amounts:

wife:son:daughter = 20:12:9

Now let the three amounts be 20x, 12x, and 9x.

We know the wife's share is 561,000 more than the daughter's share:

The total value of the property is

ANSWER: The value of the property is 2,091,000.

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