SOLUTION: A, B, C and D went fishing. A caught 50% more fish than B. If A gives C 20 fish, A, B and C will have the same number of fish. A, B and C together caught 4 times more fish than D.

Question 835479: A, B, C and D went fishing. A caught 50% more fish than B. If A gives C 20 fish, A, B and C
will have the same number of fish. A, B and C together caught 4 times more fish than D. They
kept 20% of the fish they caught, sold the rest at 200 sum per fish and shared the money equally.
How much money did each take home?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A, B, C, and D went fishing.
let a = amount of fish A caught.
let b = amount of fish B caught.
let c = amount of fish C caught.
let d = amount of fish D caught.

A caught 50% more fish than B.
This means that a = b + .5b which means that a = 1.5b.

If A gives 20 fish to C, then A, B, and C will have the same number of fish each.
This means that a - 20 = b = c + 20.

A + B + C together caught 4 times more fish than D.
This means that a + b + c = 4d.

we know that a = 1.5b
we also know that a - 20 = b
if we substitute 1.5b for a in the second equation, we get:
1.5b - 20 = b
subtract b from both sides of this equation and add 20 to both sides of this equation to get:
1.5b - b = 20
simplify to get:
.5b = 20
divide both sides of this equation by b to get:
b = 40

since a = 1.5b, this means that:
a = 60

since c + 20 = b, this mean that:
c + 20 = 40
subtract 20 from both sides of this equation to get:
c = 20

we now have:
a = 60
b = 40
c = 20

we also know that a + b + c = 4d.
a + b + c = 120
120 = 4d
divide both sides of this equation by 4 to get:
120/4 = d which means that:
d = 30

we now have:
a = 60
b = 40
c = 20
d = 30

the total is 150.
they keep 20% which means they keep 30.
that means they sold 120 at 200 apiece.
that means they received 120 * 200 = 24000
they divided it equally which means they divided 24000 by 4 to get 6000 apiece.

that last statement could possibly be interpreted differently.
the statement i am talking about is:
"A, B and C together caught 4 times more fish than D."

my own wording for that statement would have been:
"A, B, and C together caught 4 times as many fish as D."
That is the interpretation I used.
My answer is based on that interpretation.

The second interpretation would lead to a different answer.

the statement:
"A, B, and C, together, caught 4 times more fish than D." can be interpreted as follows:

They caught 4 times more fish than D.
This means they caught 5 times as many fish as D caught.
If D catches 1 fish and they catch 5 fish, then they caught 4 times more fish than D because 5 minus 1 is equal to 4 which is 4 times 1.
If D catches 2 fish and they catch 10 fish, then they caught 4 times more fish than D because 10 minus 2 = 8 which is 4 times 2.

Under this alternate interpretation, the answer would be changed as follows:
starting from "we also know that":
we also know that a + b + c = 4d + d which is equal to 5d.
a + b + c = 120
120 = 5d
divide both sides of this equation by 5 to get:
120/5 = d which means that:
d = 24
this means that:
d = 24
a + b + c = 5d = 120
120 - 24 = 96
96 = 4 * 24.
they caught 5 times more fish than D caught.

we now have:
a = 60
b = 40
c = 20
d = 24

the total is 144.
they keep 20% which means they keep 28.8
that means they sold 115.2 at 200 apiece.
that means they received 115.2 * 200 = 23040
they divided it equally which means they divided 23040 by 4 to get 5760 apiece.

this alternate interpretation does not divide as evenly as the first interpretation.
that makes it a little more doubtful that this interpretation is what they meant.

I believe the wording of the statement:
"A, B and C together caught 4 times more fish than D"
should have been worded as, and may have been meant to be worded as:
"A, B, and C together caught 4 times as many fish as D caught."

I recommend to go with the original solution because I think that's what they meant.

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