1.the sum of two numbers is 94 and their difference is 14. find the numbers
2. find two numbers whose sum is 73 and whose difference is 7
3.either 10 pens and 4 pencils, or 18 pencils and 6 pens can be bought for $78, what is the price of each?
4. a chicken and a duck cost $45,while 5 chickens and 6 ducks cost $250. find the price of each animal
5. three pens and two rubbers together cost $52. the cost of a rubber is two-thirds the cost of a pen. find the cost of a pen and a rubber
6.two articles cost $51 together and one is $3 cheaper than the other. find the cost of each article.
7. one-sixth of the sum of two numbers is 3, and eight times their difference is 32. find the numbers
8.find two numbers such that four times the first and three times the second together make 65, while twice the first together with six times the second make 82
9.the difference between two number is 5. if the larger number is added to twice the smaller number, the sum is 59.find the numbers
10.the difference of two numbers is four-fifths of their sum, and the bigger number exceeds six times the smaller number by 21.find the numbers
11.find a fraction which is equal to 3份之2 if 2 is subtracted from both the numerator and denominator,and equal to 7分之6 if 2 is added to both numerator and denominator .
英文數..唔識做
2012-09-08 3:27 am
回答 (3)
2012-09-08 4:34 am
✔ 最佳答案
1.Two numbers : a and b
a + b = 94 ... [1]
a - b = 14 ... [2]
[1] + [2] :
2a = 108
a = 54
[1] - [2] :
2b = 80
b = 40
54 and 40.
2.
Two numbers : a and b
a + b = 73 ... [1]
a - b = 7 ... [2]
[1] + [2] :
2a = 80
a = 40
[1] - [2] :
2b = 66
b = 33
40 and 33.
3.
pen : $a, pencil : $b
10a + 4b = 78 ... [1]
6a + 18b = 78 ... [2]
[1] = [2] :
10a + 4b = 6a + 18b
6a = 21b ... [3]
[3] → [2] :
21b + 18b = 78
b = 2
[3] :
6a = 21*2
a = 7
pen : $7, pencil : $2
4.
Chicken : $c, duck : $d
c + d = 45 ... [1]
5c + 6d = 250 ... [2]
[1] * 6 :
6c + 6d = 270 ... [3]
[3] - [2] :
c = 20
Put c = 20 into [1] :
20 + d = 25
d = 25
chicken : $20, duck : $25.
5.
pen : $p, rubber : $r
3p + 2r = 52 ...... [1]
r = (2/3)p ...... [2]
Put [2] into [1] :
3p + 2(2/3)p = 52
p = 12
Put p = 12 into [2] :
r = 8
pen : $12, rubber : $8.
6.
costs : $c, $e
c + e = 51 ... [1]
c = e - 3 ... [2]
Put [2] into [1] :
(e - 3) + e = 51
2e = 54
e = 27
Put e = 27 into [2] :
c = 27 - 3
c = 24
$24, $27.
7.
Two numbers : a and b
(1/6)(a + b) = 3 ... [1]
8(a - b) = 32 ... [2]
[1] :
a + b = 18 ... [3]
[2] :
a - b = 4 ... [4]
[3] + [4] :
2a = 22
a = 11
[3] - [4] :
2b = 14
b = 7
7 and 11.
8.
Two numbers : a, b
4a + 3b = 65 ... [1]
2a + 6b = 82 ... [2]
[2] * 2 - [1] :
9b = 99
b = 11
Put b = 11 into [1] :
a = 8
8 and 11
9.
Two numbers : a, b
a - b = 5 ... [1]
a + 2b = 59 ... [2]
[2] - [1] :
3b = 54
b = 18
Put b = 18 into [1] :
a = 23
18 and 23
10.
Two numbers : a, b
a - b = (4/5)(a + b) ... [1]
a - 6b = 21 ... [2]
[1] :
5a - 5b = 4a + 4b
a - 9b = 0 ... [3]
[2] - [3] :
3b = 21
b = 7
Put b = 7 into [3] :
a = 63
7 and 63
11.
Fraction : n/d
(n - 2)/(d - 2) = 2/3 ... [1]
(n + 2)/(d + 2) = 6/7 ... [2]
From [1] :
3(n - 2) = 2(d - 2)
9n - 6d = 6 ... [3]
From [2] :
7(n + 2) = 6(d + 2)
7n - 6d = -2 ... [4]
[3] - [4] :
2n = 8
n = 4
Put n = 4 into [4] :
d = 5
4/5
參考: 賣女孩的火柴
2012-09-08 8:46 am
To HO Tung (002) :
3.
You answer is wrong. Put your answer x = 2 and y = 14.5 into (2) :
L.S. = 6*2 + 18*14.5 = 273 ≠ R.S.
11.
You have not done it yet.
3.
You answer is wrong. Put your answer x = 2 and y = 14.5 into (2) :
L.S. = 6*2 + 18*14.5 = 273 ≠ R.S.
11.
You have not done it yet.
2012-09-08 5:14 am
1) Let x be the large no. ,
x+(x-14)=94
2x=108
x=54//
The nos. are 54 and 40.
2) Let x be the large no.,
x+(x-7)=73
2x=80
x=40//
The nos. are 40 and 33.
3) Let x be the price of a pen and y be the price of a pencil,
10x+4y=78 -- (1)
6x+18y=78 -- (2)
(2)*10-(1)*6,
156x=312
x=2
put x=2 into (1)
10(2)+4y=78
y=29/2
The price of a pen is $2 and the price of a pencil is $14.5.
4) Let x be the price of a chicken and y be the price of a duck,
x+y=45 --(1)
5x+6y=250 --(2)
From(1), x=45-y -- (3)
put (3)into(2), 5(45-y)+6y=250
225-5y+6y=250
y=25
put y=25into (3)
x=45-25
x=20
The price of a chicken is $20 and the price of a duck is $25.
5)
Let x be the cost of a pen and y be the cost of a rubber,
3x+2y=52 --(1)
y=2x/3 --(2)
put (2)into (1), 3x+2(2x/3)=52
3x+4x/3=52
9x+4x=156
x=12
put x=12 into (2),
y=2(12)/3
y=8
The cost of a pen is $12 and the cost of a rubber is $8.
6)
Let x be the cheaper one of the articles,
x+(x+3)=51
2x+3=51
x=24
The two article are cost $24 and $27.
7)
Let x and y be the two nos.,
(x+y)(1/6)=3 --(1)
(x-y)8 =32 --(2)
From(1), x+y=18
x=18-y --(3)
put (3)into (2), (18-y-y)8=32
144-16y=32
y=7
put y =7into(3),
x=18-7
x=11
The two nos. are 11 and 7.
8)
Let x be the first no. and y be the second no.,
4x+3y=65 --(1)
2x+6y=82 --(2)
(2)*4-(1)*2, 18y=198
y=11
put y=11 into (1),
4x+3(11)=65
x=8
The two nos. are 8 and 11.
9)
Let x be larger no. ,
x+2(x-5)=59
3x-10=59
x=23
The two nos. are 23 and 18.
10)
Let x be the bigger no. and y be the smaller no.,
x-y=(x+y)(4/5) --(1)
x-6y=21 --(2)
From (2), x=21+6y --(3)
put (3) into (1),
5x-5y=4x+4y
x-9y=0
21+6y-9y=0
y=7
put y=7 into (3),
x=21
x+(x-14)=94
2x=108
x=54//
The nos. are 54 and 40.
2) Let x be the large no.,
x+(x-7)=73
2x=80
x=40//
The nos. are 40 and 33.
3) Let x be the price of a pen and y be the price of a pencil,
10x+4y=78 -- (1)
6x+18y=78 -- (2)
(2)*10-(1)*6,
156x=312
x=2
put x=2 into (1)
10(2)+4y=78
y=29/2
The price of a pen is $2 and the price of a pencil is $14.5.
4) Let x be the price of a chicken and y be the price of a duck,
x+y=45 --(1)
5x+6y=250 --(2)
From(1), x=45-y -- (3)
put (3)into(2), 5(45-y)+6y=250
225-5y+6y=250
y=25
put y=25into (3)
x=45-25
x=20
The price of a chicken is $20 and the price of a duck is $25.
5)
Let x be the cost of a pen and y be the cost of a rubber,
3x+2y=52 --(1)
y=2x/3 --(2)
put (2)into (1), 3x+2(2x/3)=52
3x+4x/3=52
9x+4x=156
x=12
put x=12 into (2),
y=2(12)/3
y=8
The cost of a pen is $12 and the cost of a rubber is $8.
6)
Let x be the cheaper one of the articles,
x+(x+3)=51
2x+3=51
x=24
The two article are cost $24 and $27.
7)
Let x and y be the two nos.,
(x+y)(1/6)=3 --(1)
(x-y)8 =32 --(2)
From(1), x+y=18
x=18-y --(3)
put (3)into (2), (18-y-y)8=32
144-16y=32
y=7
put y =7into(3),
x=18-7
x=11
The two nos. are 11 and 7.
8)
Let x be the first no. and y be the second no.,
4x+3y=65 --(1)
2x+6y=82 --(2)
(2)*4-(1)*2, 18y=198
y=11
put y=11 into (1),
4x+3(11)=65
x=8
The two nos. are 8 and 11.
9)
Let x be larger no. ,
x+2(x-5)=59
3x-10=59
x=23
The two nos. are 23 and 18.
10)
Let x be the bigger no. and y be the smaller no.,
x-y=(x+y)(4/5) --(1)
x-6y=21 --(2)
From (2), x=21+6y --(3)
put (3) into (1),
5x-5y=4x+4y
x-9y=0
21+6y-9y=0
y=7
put y=7 into (3),
x=21
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