F.2 Maths questions

2009-07-07 8:48 pm
1. A number of two digits is less by 699 than 5 times the spuare of the number formed by reversing the digits, and the digit in the tens' place exceeds the other digit by one. Find the number. Answer: 21

2. A square floor is covered with carpet, except a border 0.5 m wide, round the carpet, which is covered with linoleum. The carpet and linoleum cost respectively $9 and $5 per m^2. The whole cost is $189. Find the length of the floor. answer: 15 m

3. The price of petrol is reduced by x per cent., and a man uses x per cent. more. as a result his petrol bill is reduced from $500 to $495. Find x. Answer: 10

請依明步驟

回答 (2)

2009-07-07 10:37 pm
✔ 最佳答案
1.
Let t be the tens digit and u be the units digit.

5(10u + t)2 - (10t + u) = 699 ...... (1)
t - u = 1 ...... (2)

(2):
t = u + 1 ...... (3)

Put (3) into (1):
5[10u + (u + 1)]2 - [10(u + 1) + u] = 699
5(11u + 1)2 - (11u + 10) = 699
5(121u2 + 22u + 1) - (11u + 10) = 699
605u2 + 110u + 5 - 11u - 10 = 699
605u2 + 99u - 704 = 0
55u2 + 9u - 64 = 0
(u - 1)(55u + 64) = 0
u = 1 or u = -64/55 (rejected)

Put u = 1 into (3):
t = (1) + 1
t = 2

Ans: The number is 21.


2.
Let y m the length of the floor.

Area of the carpet = (y - 2 0.5)2 m2 = (y - 1)2 m2
Area of the linoleum = [y2 - (y - 1)2] m2

Total cost:
9(y - 1)2 + 5[y2 - (y - 1)2] = 189
9(y2 - 2y + 1) + 5(y2 - y2 + 2y - 1) = 189
9y2 - 18y + 9 + 10y - 5 = 189
9y2 - 8y - 185 = 0
(x - 5)(9x + 37) = 0
x = 5 or x = -37/9 (rejected)

Ans: The length of the floor is 5 m (but NOT 15 m).


3.
Let A be original amount of petrol used,
and p be the original unit price of petrol.

Original bill:
Ap = 500 ...... (1)

New bill:
A(1 + x%)•p(1 - x%) = 495 ...... (2)

(2)/(1):
(1 + x%)(1 - x%) = 495/500
100(1 + x%) •100(1 - x%) = 100 x 100 x 495/500
(100 + x)(100 - x) = 9900
10000 - x2 = 9900
x2 - 100 = 0
(x - 10)(x + 10) = 0
x = 10 or x = -10 (rejected)

Ans: x is 10.
2009-07-07 10:48 pm
Question 1
Let the ten digit and unit digit of the number be a and b
According to the question,
a=b+1… (1)
5(10b+a)^2-(10a+b)=699…(2)

Put (1) into (2),
5[10b+b+1)^2-[10(b+1)+b]=699
5(11b+1)^2-(11b+10)=699
5(121b^2+22b+1)-(11b+10)=699
605b^2+110b+5-11b-10=699
605b^2+99b-704=0
11(55b^2+9b-64)=0
11(55b+64)(b-1)=0
So b=-64/55(reject) [b cannot be negative] or 1
b=1 =>a=2

the number is 21

Question 3
500(1-x%)(1+x%)=495
500(1-x^2/10000)=495
500-x^2/20=495
5=x^2/20
x^2=100
x=10

Question 2
Your answer must be wrong
Since the cost for carpet
= (15^2) (9) = 2,025
In exclusion of the cost of border, the total cost has already been exceeded $189 a lot.
Please check the answer again.
參考: ME


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