1. there are x red balls and y blue balls in a box. if there are altogether 72 balls, and the number of red balls is 18 less than that of blue ball, what are the number of red balls and blue balls.
2. in a box, there are 39 coins . these coins are either $2-coins or $5-coins and the sum is $123. find the number of $2-coins and $5-coins.
幾條數唔識
2011-08-24 4:24 pm
回答 (2)
2011-08-24 4:49 pm
✔ 最佳答案
1. Set up a set of simultaneous equations:x + y = 72 ----- 1
x + 18 = y ----- 2
Sub. (abbreviation of substitute) 2 into 1(1 and 2 are the equation number),
x + x + 18 = 72
2x = 54
x = 27
Substitute x = 27 into 2,
y = 27 + 18 = 45
∴ There are 27 red balls and 45 blue balls.
2. Let x be the number of $2 coins and y be the number of $5 coins.
x + y = 39 ----- 1
2x + 5y = 123 ----- 2
From 1 , x = 39 - y ----- 3
Sub. 3 into 2,
2(39 - y) + 5y = 123
78 - 2y + 5y = 123
3y = 45
y = 15
Sub. y = 15 into 3,
x = 39 - 15 = 24
∴ There are 24 $2 coins and 15 $5 coins.
參考: textbook, myself
2011-08-25 12:21 am
1.let x be the number of red balls,y be the number of blue balls.
x+y=72------(1)
x=y-18------(2)
sub (2) into (1)
y-18+y=72
2y-18=72
2y=90
y=45
sub y=45 into(2)
x=45-18
x=27
number of red balls=27
number of blue balls=45
2.let x be the number of $2 coins,y be the number of $5 coins.
2x+5y=123------(1)
x+y=39------(2)
(2)*2 2x+2y=78------(3)
(1)-(3),
2x+5y-(2x+2y)=123-78
3y=45
y=15
sub y=15 into (2)
x+15=39
x=24
Hence,number of $2 coins=24
number of $5 coins=15
x+y=72------(1)
x=y-18------(2)
sub (2) into (1)
y-18+y=72
2y-18=72
2y=90
y=45
sub y=45 into(2)
x=45-18
x=27
number of red balls=27
number of blue balls=45
2.let x be the number of $2 coins,y be the number of $5 coins.
2x+5y=123------(1)
x+y=39------(2)
(2)*2 2x+2y=78------(3)
(1)-(3),
2x+5y-(2x+2y)=123-78
3y=45
y=15
sub y=15 into (2)
x+15=39
x=24
Hence,number of $2 coins=24
number of $5 coins=15
參考: just my answer
收錄日期: 2021-04-13 18:11:41
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