Tutor MathsGuru: Ask me for your burning Maths questions!

[Sun_2010]

CoffeeCat:

Sun_2010:

Hi,


DD is struck at this question . I tried it too- cant get it.
Can some one help?
Question 6 of the sample paper for APMOS
http://www.hci.sg/aphelion/apmops/sample_questions/Invitation%20Round%20Sample%20Questions.pdf

Thanks

What a coincidence, I was explaining that question to a student at the time when you post this.
This happens to belongs to a class of geometry questions which solutions requires the construction of an equilateral triangle.
At first glance, the clue AB=DC look useless because the 2 lines are far away and usually we think of isoceles triangle when we heard of 2 equal lines in angles.
Imagine that there is a perpendicular line passing through the midpoint of BC, then reflect the triangle BDC about that line, so that there is now a new point D' in the interior of the triangle such that angle BD'C = angle CDB, and angle D'BC = angle DCB = 20 deg.
Notice CD = BD' = AB ( ABD' is isoceles) and since angle ABC=80 deg, angle ABD' = 80-20=60 deg, thus ABD' is an equilateral triangle.
We want to find angle BDC, which is equivalent to finding angle CD'B.
The next step will be hard to see if your equilateral triangle is not drawn properly, because the point D' is actually directly midway between A and B. angle BD'C = angle AD'C = (360-60)/2 = 150deg.

Thanku Thank u , Coffee cat.
I did try shifting the trangle etc , but never thought of reflecting it. Frankly it took me abt 10 full min to understand a solution u have so neatly explained. So not only is a problem solved , I have learnt a new technique. So really :salute: to u.

Ah now i can sleep in peace

[Vanilla Cake]

Sun_2010:

CoffeeCat:

[quote=\"Sun_2010\"]Hi,


DD is struck at this question . I tried it too- cant get it.
Can some one help?
Question 6 of the sample paper for APMOS
http://www.hci.sg/aphelion/apmops/sample_questions/Invitation%20Round%20Sample%20Questions.pdf

Thanks

What a coincidence, I was explaining that question to a student at the time when you post this.
This happens to belongs to a class of geometry questions which solutions requires the construction of an equilateral triangle.
At first glance, the clue AB=DC look useless because the 2 lines are far away and usually we think of isoceles triangle when we heard of 2 equal lines in angles.
Imagine that there is a perpendicular line passing through the midpoint of BC, then reflect the triangle BDC about that line, so that there is now a new point D' in the interior of the triangle such that angle BD'C = angle CDB, and angle D'BC = angle DCB = 20 deg.
Notice CD = BD' = AB ( ABD' is isoceles) and since angle ABC=80 deg, angle ABD' = 80-20=60 deg, thus ABD' is an equilateral triangle.
We want to find angle BDC, which is equivalent to finding angle CD'B.
The next step will be hard to see if your equilateral triangle is not drawn properly, because the point D' is actually directly midway between A and B. angle BD'C = angle AD'C = (360-60)/2 = 150deg.

Thanku Thank u , Coffee cat.
I did try shifting the trangle etc , but never thought of reflecting it. Frankly it took me abt 10 full min to understand a solution u have so neatly explained. So not only is a problem solved , I have learnt a new technique. So really :salute: to u.

Ah now i can sleep in peace :-)[/quote]Hi readers,
For your reference with a http://psle2010a.blogspot.com/2010/05/p6anglesa001.html from the always helpful Uncle Observer.

[abc_parent]

Hi,


Please help:

Russel delivered 7348 cartons of eggs to several supermarkets. For every carton of eggs safely delivered, he would have paid 80 cents. However, for every damaged carton, he would have to pay $1.40. Russel was paid a total of $5396.60

(a) How many cartons of eggs were damaged?
(b) How many cartons of eggs were delivered safely?

Ans: 219
Ans: 7129

Can you please explain step by step?

[abc_parent]

Rahim bought some key chains at 90 cents each. He sold them at $3.50 each at a 3-day charity fair. From the second day onwards, for every 4 key chains sold, 1 key chain would be given free. At the end of the fair, a total of 208 free key chains were given away. After deducting the amount of money that Rahim has paid for the key chains, the money collected for the charity was $2441.40. How many key chains were sold individually on the first day?


Ans: 179 keychains

can explain step by step? thanks!!

[small]

abc_parent:

Rahim bought some key chains at 90 cents each. He sold them at $3.50 each at a 3-day charity fair. From the second day onwards, for every 4 key chains sold, 1 key chain would be given free. At the end of the fair, a total of 208 free key chains were given away. After deducting the amount of money that Rahim has paid for the key chains, the money collected for the charity was $2441.40. How many key chains were sold individually on the first day?


Ans: 179 keychains

can explain step by step? thanks!!

Hi abc_parent,

Hopes my solution is clear enough.

For 2nd day and 3rd day, he given away 208 key chains; which means he sold:\t\t\t\t
208 x 4 = 832\t\t\t\t

Rahim sold 832 key chains altogether on 2nd and 3rd day.\t\t\t\t

Given total profit = $2441.40\t\t\t\t
Profit of one key chain = 3.5 -0.9 = $2.60\t\t\t\t
Total cost of 208 free key chains = 208 x $0.90\t\t\t\t

(832 + Number of key chains sold on 1st day) x $2.60 - (208 x $0.90) = $2441.40\t\t\t\t
(832 + Number of key chains sold on 1st day) x $2.60 = $2628.6\t\t\t\t
(832 + Number of key chains sold on 1st day) = $2628.6 / $2.60
(832 + Number of key chains sold on 1st day) = 1011
Number of key chains sold on 1st day = 1011 - 832 = 179

Rahim sold 179 key chains on the fist day.

.

[small]

abc_parent:

Hi,


Please help:

Russel delivered 7348 cartons of eggs to several supermarkets. For every carton of eggs safely delivered, he would have paid 80 cents. However, for every damaged carton, he would have to pay $1.40. Russel was paid a total of $5396.60

(a) How many cartons of eggs were damaged?
(b) How many cartons of eggs were delivered safely?

Ans: 219
Ans: 7129

Can you please explain step by step?

Hi abc_parent,

Hopes my method will not confusing you.

Lets : \t
Numer of safely delivered carton = G
Number of damaged carton = D\t\t\t\t
\t\t\t\t\t
\tG + D = 7348 ------------------> (1)\t\t\t\t
\t\t\t\t\t
\t\t\t\t\t
\t0.8G - 1.4D = 5396.6 --------> x 5\t\t\t\t
\t4G - 7D = 26983 --------------> (2)\t\t\t\t
\t\t\t\t\t
a)\tBy eliminating G to get D\t\t\t\t
\t\t\t\t\t
\t4 (7348 - D) - 7D = 26983\t\t\t\t
\t29392 - 4D - 7D = 26983\t\t\t\t
\t11D = 29392 - 26983\t\t\t\t
\t11D = 2409\t\t\t\t
\tD = 219\t\t\t\t
\t\t\t\t\t
\t219 cartons of eggs were damaged. \t\t\t\t
\t\t\t\t\t
b)\t7348 - 219 = 7129\t\t\t\t
\t\t\t\t\t
\t7129 cartons of eggs were delivered safely.

.

[Dharma]

abc_parent:

Hi,


Please help:

Russel delivered 7348 cartons of eggs to several supermarkets. For every carton of eggs safely delivered, he would have paid 80 cents. However, for every damaged carton, he would have to pay $1.40. Russel was paid a total of $5396.60

(a) How many cartons of eggs were damaged?
(b) How many cartons of eggs were delivered safely?

Ans: 219
Ans: 7129

Can you please explain step by step?

Assume every carton of eggs is safely delivered

Russel earned = 7348 x $0.80 = $5,878.40

No. of cartons of eggs damaged = ($5,878.40 - $5,396.60)/ ($0.80 + $1.40) = 219
No. of cartons delivered safely = 7348 – 219 = 7129

[abc_parent]

Hi, thanks to Dharma and small.

Can you see this question too?

Mr F drove from home to work at 60km/h . After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he tool 5 minutes less than what he had taken on his way to work. What was the distance between his house and office?

Ans given: 15km

I think should be 90km.

[Dharma]

abc_parent:

Hi, thanks to Dharma and small.

Can you see this question too?

Mr F drove from home to work at 60km/h . After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he tool 5 minutes less than what he had taken on his way to work. What was the distance between his house and office?

Ans given: 15km

I think should be 90km.

Distance between his house and office is fixed, Speed is inversely proportional to the time taken.
Speed ratio = 2 : 3
Time ratio = 3 : 2
3u – 2u = 1u = 5/60 = 1/12 hrs (Difference in time taken)

Distance = 60km/h x 3 x 1/12hrs = 15km

[abc_parent]

Lily, Mina and Oscar each donated some money to charity. The donation made by Lily was 2/3 as much as the total amount donate by Mina and Oscar. Mina donated 1/5 as much as the total donated by Lily and Oscar. If Oscar donated $360 more than Mina, how much did Lily donate?


Ans: $540

Ali, Bala and Charles shared a tin of cookies. Ali took 5/6 of the tin of cookies and 1/3 of a cookie. Bala took 5/6 of the remaining tin of cookies and 1/3 of a cookie. Charles received only 2 cookies. How many more cookies did Ali have than Bala?

Ans: 60

Please help me by explaining step by step. Thanks in advance !

Thanks to Dharma for helping me with my last question!!!