Form two 數\”二元一次方\”(With answer)

︾ｓｈａｎ＊︽

2010-03-06 7:40 am

要列式and 解方程!!thank you!!!!!!!!!!!!!!!

(請用substitution or elimination to solve the simultaneous equation!!)

16.the sum of the digits of a 2-digit number is12.if the two digits are reversed,the value of the number is decreased by 36.find the original number.

(Answer 84)
17.in a 2-digit number,the tens digit is 5 more than the units digit.find the 2-digit
number if it is equal to the product of the units digit and 36.

(Answer 72)
18 .in a 2-digit number ,the ten digit is 2 more than the units digit.if the 2-digit
number is divided bu the sum of the 2 digits,the quotient is7.Find the original
2-digit number

(Answer 42)

19.there is a square and an equilateral triangle,their perimeter is the same.
(the length of the square is (2x+y-2)cm
the width底 of the equilateral triangle is (x+2y+11)cm:三角形的邊是(2x+y+1)cm
)
(a)the value of "x" and "y''
(Answer X=7,y= - 3)

(b)the area of the square

(Answer 81 cm^3)
26.the following table shows Billy's mobile phone service charges.

the charge of the voice connection is $0.6 per minute
the charge of the video connection is $0.8 per minute

(a)last month,Billy's mobile phone charge was $400.thi month ,his usage of
voice connection drcreased by 40％ and his usage of video connection incresed
by 20％.AS a result ,his mobile phone charge decreased by 16％ this month.
Find the actual usage of video and voice connection this month.

(Answer Video=240min:voice=240min)

更新1:

sorry!!可可可以做多兩條challenging question? 46.the solution of the simultaneous equation x+y=4x-y=5 is x=2,y=3. (b) Hence solve the simultaneous equation 1/a+1/b=4/a-1/b=5 (answer,x=2,y=3) 54.give that 1/a-1/b=X/a-b and a/b+b/a=Y,Find Y in terms of X. (answer,Y=2-X) 萬份感謝!!!!!!!!

回答 (1)

老爺子

2010-03-06 10:44 am

✔ 最佳答案

16.
Let t be the tens digit of the original number, and u be the units digit.

t + u = 12 ... (1)
(10u + t) = (10t + u) - 36 ... (2)

(1):
t = 12 - u ... (3)

Put (3) into (2):
[10u + (12 - u)] = [10(12 - u) + u] - 36
10u + 12 - u = 120 - 10u + u - 36
18u = 72
u = 4

Put u = 4 into (3):
t = 12 - 4
t = 8

The original number = 84

17.
Let t be the tens digit of the original number, and u be the units digit.

t = 5 + u ... (1)
10t + u = 36u ... (2)

Put (1) into (2):
10(5 + u) + u = 36u
50 + 10u + u = 36u
25u = 50
u = 2

Put u = 2 into (1):
t = 5 + 2
t = 7

The original number = 72

18.
Let t be the tens digit of the original number, and u be the units digit.

t = u + 2 ... (1)
(10t + u)/(t + u) = 7 ... (2)

Put (1) into (2):
[10(u + 2) + u]/[(u + 2) + u] = 7
(10u + 20 + u)/(u + 2 + u) = 7
11u + 20 = 7(2u + 2)
11u + 20 = 14u + 14
3u = 6
u = 2

Put u = 2 into (1):
t = 2 + 2
t = 4

The original number = 42

19.
(a)
4(2x + y - 2) = 3(x + 2y + 11) ... (1)
x + 2y + 11 = 2x + y + 1 ... (2)

(1):
8x + 4y - 8 = 3x + 6y + 33
5x - 2y = 41 ... (3)

(2):
x - y = 10
2x - 2y = 20 ... (4)
5x - 5y = 50 ... (5)

(3) - (4):
3x = 21
x = 7

(3) - (5):
3y = -9
y = -3

(b)
Area of the square
= (2x + y - 2)² cm²
= [2(7) + (-3) - 2] ² cm²
= (9)² cm²
= 81 cm²

26.
Let a min be the time of voice connection, and b be the time of video connection.

0.6a + 0.8b = 400 ... (1)
0.6a(1 - 40%) + 0.8b(1 + 20%) = 400(1 - 16%) ... (2)

(1):
6a + 8b = 4000
3a + 4b = 2000 ... (3)

(2)
0.36a + 0.96b = 336
36a + 96b = 33600
3a + 8b = 2800 ... (4)

(4) - (3):
4b = 800
b = 200

Put b = 200 into (3):
3a + 4(200) = 2000
3a = 1200
a = 400

The time of the voice connection = 400 min
The time of the video connection = 200 min
(The given answers are incorrect.)

參考: 老爺子

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