math...
2007-12-28 7:41 pm
In a bag there are some $1 coins and som $2 coins. If there are altogether 60 coins and the total value of the coins is $108, what is the difference between the number of $1 coins and som $2 coins?
回答 (9)
2007-12-28 7:48 pm
✔ 最佳答案
Let there are x $1 coins and y $2 coinsx + y = 60, i.e. x = 60 - y
x + 2y = 108
60 - y + 2y = 108
60 + y = 108
y = 48
x = 60 - 48 = 12
y - x = 48 - 12 = 36
2007-12-29 12:57 am
Let x be the numbers of coins $1, then and y be the numbers of coins$2.
Because there are together are 60 coins and total value of the coins is 108 dollars,
so the solve equation are x+y=60 and x+2y=108.
Solve: x+y=60----(1) and
x+2y=108----(2)
From(1), x+y=60
x=60-y-----(3)
Put (3) into (2), we have
x+2y=108
(60-y)+2y=108
60+y=108
y=48-----(4)
Put (4) into (1), we have
x+48=60
x=12
The numbers of coins$1 is 12, and the numbers of coins$2 is 48.
The difference between the numbers of coins$1and the numbers of coins$2 are 48-12=36 , compare the numbers of coins$1 less than the numbers of coins$2 are 36.
Thank you very much!
2007-12-28 17:01:58 補充：
由於電腦程式緣故，「 " "」是代表空白而格行。
Because there are together are 60 coins and total value of the coins is 108 dollars,
so the solve equation are x+y=60 and x+2y=108.
Solve: x+y=60----(1) and
x+2y=108----(2)
From(1), x+y=60
x=60-y-----(3)
Put (3) into (2), we have
x+2y=108
(60-y)+2y=108
60+y=108
y=48-----(4)
Put (4) into (1), we have
x+48=60
x=12
The numbers of coins$1 is 12, and the numbers of coins$2 is 48.
The difference between the numbers of coins$1and the numbers of coins$2 are 48-12=36 , compare the numbers of coins$1 less than the numbers of coins$2 are 36.
Thank you very much!
2007-12-28 17:01:58 補充：
由於電腦程式緣故，「 " "」是代表空白而格行。
2007-12-28 8:47 pm
Let x be the number of $1 coins
and y be the number of $2 coins.
x + y = 60 ... (1)
x + 2y = 108 ... (2)
From (1), y = 60 - x ... (3)
Sub. (3) into (2),
x + 2(60 - x) = 108
x + 120 - 2x = 108
-x = -12
x = 12
Sub. x = 12 into (3),
y = 60 - 12
= 48
∴The difference between the number of $1 coins and the number of $2 coins
= 48 - 12
= 36
and y be the number of $2 coins.
x + y = 60 ... (1)
x + 2y = 108 ... (2)
From (1), y = 60 - x ... (3)
Sub. (3) into (2),
x + 2(60 - x) = 108
x + 120 - 2x = 108
-x = -12
x = 12
Sub. x = 12 into (3),
y = 60 - 12
= 48
∴The difference between the number of $1 coins and the number of $2 coins
= 48 - 12
= 36
2007-12-28 8:15 pm
In a bag there are some $1 coins and som $2 coins. If there are altogether 60 coins and the total value of the coins is $108, what is the difference between the number of $1 coins and som $2 coins?
Let the number of $1 coins be x and number of $2 coins be y
there are altogether 60 coins
so we have x + y = 60
x = 60 - y ........1
the total value of the coins is $108
so we have x + 2y = 108
x = 108 - 2y...........2
60 - y = 108 - 2y
y = 48
x = 60 - y
x = 60 - 48
x = 12
Hope they can help
2007-12-28 12:16:45 補充：
the difference between the number of $1 coins and som $2 coinsnumber of $1 coins : 12number of $2 coins : 4848 - 12 = 36
Let the number of $1 coins be x and number of $2 coins be y
there are altogether 60 coins
so we have x + y = 60
x = 60 - y ........1
the total value of the coins is $108
so we have x + 2y = 108
x = 108 - 2y...........2
60 - y = 108 - 2y
y = 48
x = 60 - y
x = 60 - 48
x = 12
Hope they can help
2007-12-28 12:16:45 補充：
the difference between the number of $1 coins and som $2 coinsnumber of $1 coins : 12number of $2 coins : 4848 - 12 = 36
參考: My calculation
2007-12-28 7:59 pm
imangine all of the coins are $2 coins. There will be totally$120 in the bag. But the total value of the coins is only $108. The only way to decrese these $12 is to change some of the $2 coins into $1.
After we change 12 coins into $1, we'll get12 $1 coins and48 $2 coins.Therefore,the diffrence between kinds of coins is 36.
After we change 12 coins into $1, we'll get12 $1 coins and48 $2 coins.Therefore,the diffrence between kinds of coins is 36.
2007-12-28 7:58 pm
呢個應該係二元一次方程式，
但係what is the difference between the number of $1 coins and som $2 coins?
個「som」個度我唔明，我估佢係問$1同$2數量之間o既差佢...
設袋中有X個$1和Y個$2，
「X+Y=60........(1) 《---------o個個係大括-__-
﹂X+2Y=108...(2)
由(1)，X+Y=60
X=60-Y...(3)
把(3)代入(2)，
(60-Y)+2Y=108
2Y-Y=48
Y=48
把Y=48代入(1)，
X+48=60
X=12
所以，X=12和Y=48。
$1和$2之間的差距:48-12
=36
但係what is the difference between the number of $1 coins and som $2 coins?
個「som」個度我唔明，我估佢係問$1同$2數量之間o既差佢...
設袋中有X個$1和Y個$2，
「X+Y=60........(1) 《---------o個個係大括-__-
﹂X+2Y=108...(2)
由(1)，X+Y=60
X=60-Y...(3)
把(3)代入(2)，
(60-Y)+2Y=108
2Y-Y=48
Y=48
把Y=48代入(1)，
X+48=60
X=12
所以，X=12和Y=48。
$1和$2之間的差距:48-12
=36
參考: F.2個陣學o既二元一次方程式
2007-12-28 7:49 pm
Let the number of $2 coins be x
and that of $1 coins be (80-x)
2x + (80-x) = 108
x+80 = 108
x = 28
ie the number of $1 coins and $2 coins are 52 and 28
The difference will be 52-28 = 24
and that of $1 coins be (80-x)
2x + (80-x) = 108
x+80 = 108
x = 28
ie the number of $1 coins and $2 coins are 52 and 28
The difference will be 52-28 = 24
2007-12-28 7:48 pm
Let the number of of $1 and $2 coins are u and v respectively
u + v =60 ............ (1)
u + 2v = 108 ............ (2)
Therefore,
(2) -(1) gives
(u+2v) - (u+v) = 108 - 60
v = 48
Substitute v=48 into (1)
u + 48 = 60
u = 12
Therefore, there are 12 one dollar coins and 48 two dollar coins.
2007-12-28 11:49:38 補充：
And the difference between the number of $1 coins and $2 coins is48 -12 = 36
u + v =60 ............ (1)
u + 2v = 108 ............ (2)
Therefore,
(2) -(1) gives
(u+2v) - (u+v) = 108 - 60
v = 48
Substitute v=48 into (1)
u + 48 = 60
u = 12
Therefore, there are 12 one dollar coins and 48 two dollar coins.
2007-12-28 11:49:38 補充：
And the difference between the number of $1 coins and $2 coins is48 -12 = 36
2007-12-28 7:48 pm
let the number of $1 coins be X and number of $2 coins beY
X+Y=60---1
X+2Y=108---2
1-2:-Y=-48
Y=48
Sub it into 1
X+48=60
X=12
the difference between the number of $1 coins and $2 coins=48-12=36
X+Y=60---1
X+2Y=108---2
1-2:-Y=-48
Y=48
Sub it into 1
X+48=60
X=12
the difference between the number of $1 coins and $2 coins=48-12=36
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