MATHS...simultaneous equation

2010-07-17 7:29 pm

1.The ten digit and the units digit of a two-digit number are x and y respectively.
The product of the two digits is 35 . If we reverse the positions of the two digits
in the number, the new tow-digit number will be 18 less than the original number.

(a)Find the two equations connecting x and y.
(b)Hence find the original two-digit number.

ANS is (b) 75

11.A cyclist has a choice of two routes for a journey. One is 24 km and the
other one is 20 km. If he chooses the longer route, his cycling speed can be 4
km/h faster than what it is in the other route, and as a result he can finish the
journey 30 minutes earlier. How long does it take for the cyclist to finish the
journey by the longer route.

ANS is 2 hours

12(a).Slove the equation 10x^2+19x-33=0.
12(b).Tom deposited $1000 and $1900 in a bank on his 20th birthday and 21st
birthday respectively. The interest was compounded yearly at r% p.a., and the
total amount hr received on his 22nd birthday was $3300.Find the value of r.

ANS is (a) x=-3 or 11/10
(b) r=10

THX!!!

回答 (1)

石石

2010-07-17 8:42 pm

✔ 最佳答案

1.(a)
xy=35
(10y+x)+18=10x+y

(b)
xy=35 ... (1)
(10y+x)+18=10x+y ... (2)

From(2), 9y=9x-18 => y=x-2 ... (3)

Sub. (3) into (1),
x(x-2)=35
x^2-2x-35=0
(x-7)(x+5)=0
x=7 or -5(rej.)

Sub x=7 into (1),
7y=35
y=5

Therefore, the no. is 75

11.
Let t h be the time needed for the longer route, then (t+1/2) h is the time needed for the other route.

24 / t = 20 / (t+1/2) + 4
12 / t = 10 / (t+1/2) + 2
12(t+1/2) = 10(t) + 2t(t+1/2)
12t + 6 = 10t + 2t^2 + t
2t^2 - t - 6= 0
(2t+3)(t-2)= 0
t= 2 or -3/2(rej.)

Therefore, it takes 2 hours.

12.(a)
10x^2+19x-33=0
(10x-11)(x+3)=0
x= 11/10 or -3

(b)
[1000*(1+r)+1900](1+r)=3300 .. (*)

Let y be (1+r),

(*) becomes
(1000y + 1900)y=3300
1000y^2+1900y=3300
10y^2+19y=33
10y^2+19y-33=0

From the results of (a) y=-3 or 11/10, that is,
1+r = -3 or 11/10 => r = -4(rej.) or 1/10

2010-07-17 12:42:34 補充：
plz check if the answer "(b) r=10" is wrong

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