O-Level Additional Math

[lost boy]

Hi, can someone help me answer these two Secondary 3 Questions…


1. A motorist started driving from Point G to Point H which is 188km apart. he travelled 30km at an average speed of x km/hr for the first part of the journey. The average speed increased by 12km/hr for the rest of the journey. Given that he took 1.5hrs to complete his journey, find the speed for the first part of the journey, giving your answer corrected to three significant figures.

2. A housewife planned to buy 430 worth of vegetables at x cents/kg.

(E) Write down an expression, in terms of x, for the number of kg she planned to buy.

(F) She found that the price of vegetables had decreased by 6 cents/kg. write down an expression in terms of x for the number of kg she can buy for $30 now.

(G) Given that she actually bought 5 5/9kg more than she had planned, form an equation in x and show that it reduces to x^2 - 6x - 3240 =0.

(H) Solve the above equation and use your answer to find the number of kg of vegetables she bought after the price had decreased.

Thank you.

P.S. : Please show the working for the respective questions.

[jieheng]

lost boy:

Hi, can someone help me answer these two Secondary 3 Questions...


1. A motorist started driving from Point G to Point H which is 188km apart. he travelled 30km at an average speed of x km/hr for the first part of the journey. The average speed increased by 12km/hr for the rest of the journey. Given that he took 1.5hrs to complete his journey, find the speed for the first part of the journey, giving your answer corrected to three significant figures.

P.S. : Please show the working for the respective questions.

Time = Distance / Speed

Time taken for the first part of the journey = 30 / x

Time taken for the rest of the journey = (188-30) / (x+12) = 158 / (x+12)

30/x + 158/(x+12) = 1.5
[ 30(x+12) + 158x] / [x(x+12)] = 3/2
(188x + 360 ) / (x^2 + 12x) = 3/2
376x + 720 =3x^2 + 36x
3x^2 - 340x - 720 = 0

x = {340 ± square_root [ (-340)^2 - 4 (3)(-720)] } / 6
= (340 ± 352.48 ) / 6

x = 115 or x = -2.08 (rej)

Ans : The speed of the first part of the journey is 115 km/h

[jieheng]

lost boy:

2. A housewife planned to buy $30 worth of vegetables at x cents/kg.

(E) Write down an expression, in terms of x, for the number of kg she planned to buy.

(F) She found that the price of vegetables had decreased by 6 cents/kg. write down an expression in terms of x for the number of kg she can buy for $30 now.

(G) Given that she actually bought 5 5/9kg more than she had planned, form an equation in x and show that it reduces to x^2 - 6x - 3240 =0.

(H) Solve the above equation and use your answer to find the number of kg of vegetables she bought after the price had decreased.

Thank you.

P.S. : Please show the working for the respective questions.

$30 = 3000 cents

E) the number of kg she planned to buy = 3000 / x

F) the number of kg she can buy for $30 now = 3000 / (x-6)

5 5/9kg = 50 / 9 kg

G)

3000/(x-6) - 3000/x = 50/9
[3000x-3000(x-6)] / [x(x-6)] = 50/9
18000 / (x^2 - 6x) = 50/9
360 / (x^2 - 6x) = 1/9
x^2 - 6x = 3240
x^2 - 6x - 3240 = 0 (Shown)

H)

x^2 - 6x - 3240 = 0
(x-60)(x+54) = 0
x = 60 or x = -54 (rej)

the number of kg of vegetables she bought after the price had decreased
= 3000 / (x-6)
= 3000 / (60-6)
=3000 / 54
=55.6 (Ans)

[lost boy]

Thank you for your help Jieheng.

[Michaelia0816]

Need help with this Sec 1 Factor and Multiple Question:


3 faulty light bulbs which flickers a intervals of 6,45 and x minutes respectively. If all of them flickers at the same time at 3 minutes interval, find the smallest possible value of x?

Sources:
From Pasir Ris Sec School Paper

[Skyed]

Michaelia0816:

Need help with this Sec 1 Factor and Multiple Question:


3 faulty light bulbs which flickers a intervals of 6,45 and x minutes respectively. If all of them flickers at the same time at 3 minutes interval, find the smallest possible value of x?

Sources:
From Pasir Ris Sec School Paper

Do you mean \"flickers at intervels of 6,45 and x SECONDS respectively\"? Because otherwise the question doesn't make sense.

[Michaelia0816]

Sorry, u r correct. It should be at intervals of 6,45, x minutes respectively.

[Michaelia0816]

Skyed:

Michaelia0816:

Need help with this Sec 1 Factor and Multiple Question:


3 faulty light bulbs which flickers at intervals of 6,45 and x minutes respectively. If all of them flickers at the same time at 3 minutes interval, find the smallest possible value of x?

Sources:
From Pasir Ris Sec School Paper

Do you mean \"flickers at intervels of 6,45 and x SECONDS respectively\"? Because otherwise the question doesn't make sense.

Pls help me with this question. I had changed the corrections.

[Skyed]

The correction are you sure it’s not seconds? Because I don’t think it’s minutes.

[Michaelia0816]

I have common test tmr, can help me with this challenging questions:


1.Given that the HCF of 30,100 and x is 10 and x is not equal to 10, find 3 possible values of x less than 150.

2. Given that the LCM of 5,14 and y is 140, find 3 possible of y.

3.Find the smallest positive integer n for which perfect cube 2750n is a whole number.

4. Rashid had sweets of 3 different flavours. There were 99 strawberry flavoured, 42 orange flavoured and 141 lemon flavoured sweets. He packed an equal number of each flavour into small packet but 1 strawberry and 1 lemon flavoured sweets were left out.
(a) (i) What was the maximum number of packets?
(ii) How many sweets were there in each small packets?

(b) If all sweets were included,
(i) what was the maximum number of packets
(Ii) how many sweets were there in each packet