P.6 maths

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let x be the amount of money A must give to B

200-X=3(40+X)
200-X=120+3X
200-X+X=120+3X+X
200=120+4X
200-120=120+4X-120
80=4X
20=X
X=20
so A must give $20 to B

A 有$200, B 有$40, 多少必須A 授予對B 以便A's 金錢是B's 的3 次?

A has $200, B has $40, how much must A give to B so that A's money is 3 times of B's?

A has $200 and B has $40
the sum of money of A and B is
=$200 +$40
=$240

Given that, A's money is 3 time of B's money.
Because A's money : B's money = 3:1
And the sum of money And B is $240
Then, A's money : B's money = $180:$60
Therefore, A gives $20 to B so that A's money is 3 times of B's

Let amounts of money of A and B be $x and $y respectively after A gives B the money.

The sum of their money is $240 which can be wrote as x+y=240.
A's money is 3 times of B's can be wrote as x=3y.

From two equations above, we can use the method of simultaneous equation to solve it.
i.e., {x+y=240......(1)
　 {x=3y......(2)

sub. (2) into (1), 3y+y=240
　　　　　　　 4y=240
　　　　　　　 y=60

sub. y=60 into (2),　x=180
∴ The amounts of money of A and B are $180 and $60 respectively after A gives B the money.

Compare with the original amount of money of A,
A must give $200-$180=$20 to B so that A's money is 3 times of B's.