Tutor MathsGuru: Ask me for your burning Maths questions!

[SoWoW]

Help needed for the following questions:


Q1 : Tom and Jerry each has some money. If Tom spends $90 per day and jerry spends $45 per day, Tom will have $1100 left when Jerry has spent all his money. If Tom spends $45 each day and Jerry spends $90 each day. Tom will have $1700 left when Jerry has spent all his money. How much did Jerry have?

Q2 : Ravi had a total of 204 goldfish and swordtails in the ratio of 9:8. After she gave away an equal number of each type of fish , the number of goldfish and swordtails left was in the ratio of 9:5 respectively. What was the total number of fish that she had given away?


Q3: Aifang, Bala and Cindy shared some sweets. Aifang received 1/11 of the sweets. Bala received 1/4 of the number of sweets Cindy received. When cindy gave away 104 sweets to be shared between Aifang and Bala, they found that all of them had the same number of sweets. How many sweets were there at first?

[tinasen]

Hi ADoc,

I was going through the same problem (3) as below. I couldn't get how the net total remains unchanged as either the white or dark chocolates get eaten up. Would it mean -3 from total in either case. I also checked the another problem in couple of pages back about the red and blue marbles. In the marble problem case, I could understand as it's a mere replacement. Can pls help me to clarify?

- Thanks.
Tina

ADoc:

Apphia:

1) Mr Indra is 48 yrs old and his son is 14 yrs old now. How many years later will Mr Indra be twice the age of his son?

2) A pet shop owner bought some cans of dog food. He divided the dog food equally among his dogs. If he bought 7 cans for each dog, he would have bought 4 extra cans. If he bought 11 cans for each dog, he would need 28 more cans.
a)How many dogs were there in the pet shop?
b) How many cans did the owner buy?

3) Mr Chen sold golf balls in packs of 6. The selling price of each pack of golf balls was $22. He sold 60% of his golf balls at $22 per pack and the rest at a discount of 50%. He collected $2640 from the sale of all the golf balls. How many golf balls did he sell altogether?

4) Siti has some dark chocolates and white chocolates in a container. If she eats 3 dark chocolates, the ratio of the number of dark chocolates to the number of white chocolates will become 5:4. If she eats 3 white chocolates, the ratio of the number of dark chocolates will then be 7:5. What is the original number of dark chocolates and white chocolates in the container?

5)Given that 12:28 = ? : 21, what is the number in the ?

Sorry for asking so many questions.

Thank you so much.

Hi! Quick answers..pls let me know if you require the models (some questions do not) for clarity. I love drawing them anway but guess it's an overkill sometimes. cheers!

(1) Key Concept: the difference between the ages remains constant (hence increase the ratio by some multiple so that the difference between the ratio units are the same as before)

now
Indra : Son = 48 : 14 (difference = 48-14 = 34)
years later
Indra : Son = 2 : 1 (difference = 2-1 = 1, but we need 34)
= (2 x 34) : (1 x 34) = 68 : 34
ans = 68 - 48 = 20 yrs' time or 34 - 14 = 20

(2) there's some problem with the wording of the question but here's my suggested solution anyway based on the typical mode of such questions.

number of dogs = D units
7 cans, 4 extra --> total cans he bought = 7D + 4
11 cans, 28 short --> total cans he bought = 11D - 28 [minus 28 because 11D is 28 more than the total number of cans he bought]

since no change in cans, therefore 7D + 4 = 11D - 28
--> 4D = 32, therefore D = 8
Ans = 8 dogs
He bought 8 x 7 + 4 = 60 cans

(3) key concept: converting ratio units to ratio in terms of worth (i.e. $)

number of $22 packs sold : number of 50% ($11) packs = 6 : 4 = 3 : 2 (must be able to convert between equivalent ratio --> fraction --> percentage)

ratio of sales revenue ($) from $22 pack : ratio of sales revenue ($) from $11 pack = (3 x 22) : (2 x 11) = 3 : 1 (4 Units)

4Units --> $2640
1Unit --> $2640/4 = $660, therefore 3Units --> $660 x 3 = $1980
number of $22 packs sold = 1980/22 = 90 number of $11 packs sold = 660/11 = 60
ans = total number of packs x 6 balls = (90 + 60) x 6 = 150 x 6 = 900 [rem to check that $22 packs = 60% of total number of packs in case you arrive at the wrong answer, since there are a number of combinations of $22 & $11 packs that will give $2640]

(4) shall leave you to solve on your own. refer to a couple of pages back.
key concept: the number of units remains unchanged after subtracting either 3 white or 3 dark chocolates (take note if question changes to subtraction of different numbers)

(5) key concept: equivalent ratios (factors & multiples)
12 : 28 = ? : 21

12 : 28 = 3 : 7 = (3 x 3) : (7 x 3) = 9 : 21
ans: ? = 9

alternative if you are familiar with ratios & fractions (including percentages) already ---> (? / 12) = (21 / 28) ....

[fxchow]

Hi,


Can someone help in this question. TIA

5 friends were playing Wii games on a Friday afternoon from 3 p.m to 6 p.m.
As there were only 4 consoles, they took turns to play.
At any time, 3 of them played while the other 2 friends watched.
If each of them had the same amount of playing time, how many minutes did each child play that afternoon?

Ans: 108 minutes

[MathIzzzFun]

fxchow:

Hi,


Can someone help in this question. TIA

5 friends were playing Wii games on a Friday afternoon from 3 p.m to 6 p.m.
As there were only 4 consoles, they took turns to play.
At any time, 3 of them played while the other 2 friends watched.
If each of them had the same amount of playing time, how many minutes did each child play that afternoon?

Ans: 108 minutes

Hi fxchow,

Total available play time = 3 x 3 h = 9h

So, each will get to play for 9h/5 = 9 x 60 /5 = 108min

cheers.

[MathIzzzFun]

SoWoW:

Help needed for the following questions:


Q1 : Tom and Jerry each has some money. If Tom spends $90 per day and jerry spends $45 per day, Tom will have $1100 left when Jerry has spent all his money. If Tom spends $45 each day and Jerry spends $90 each day. Tom will have $1700 left when Jerry has spent all his money. How much did Jerry have?

Q2 : Ravi had a total of 204 goldfish and swordtails in the ratio of 9:8. After she gave away an equal number of each type of fish , the number of goldfish and swordtails left was in the ratio of 9:5 respectively. What was the total number of fish that she had given away?


Q3: Aifang, Bala and Cindy shared some sweets. Aifang received 1/11 of the sweets. Bala received 1/4 of the number of sweets Cindy received. When cindy gave away 104 sweets to be shared between Aifang and Bala, they found that all of them had the same number of sweets. How many sweets were there at first?

Hi

Hope this helps :lol:

Q1 - http://www.flickr.com/photos/62167097@N02/5704049418/in/photostream

Q2 - http://www.flickr.com/photos/62167097@N02/5703483755/in/photostream

Q3 - http://www.flickr.com/photos/62167097@N02/5702496453/in/photostream

cheers.

[fxchow]

MathIzzzFun:

fxchow:

Hi,


Can someone help in this question. TIA

5 friends were playing Wii games on a Friday afternoon from 3 p.m to 6 p.m.
As there were only 4 consoles, they took turns to play.
At any time, 3 of them played while the other 2 friends watched.
If each of them had the same amount of playing time, how many minutes did each child play that afternoon?

Ans: 108 minutes

Hi fxchow,

Total available play time = 3 x 3 h = 9h

So, each will get to play for 9h/5 = 9 x 60 /5 = 108min

cheers.

Hi MathIzzzFun,

Thank you very much

[Superbugs]

Hi there, appreciate it that someone can assist me on the following questions:


Q1) There are 8 stacks of chairs and 12 chairs in each stack. Each chair is equally spaced apart to form the perimeter of a rectangle. If the no. of chairs placed along its length is thrice the no. of chairs placed along its breadth, how many chairs are placed equally along one of the length of the rectangle.

12x9 = 108
108-4 (4 corners) = 104
108/8 = 13
13x3=39
39+2 (2 corners) = 41

But the answer is 42 and instead of minusing the 4 corners, they add the 4 corners
108+4=112
112/8=42
Why is that so?

Q2) J bought some strawberries and wanted to put them in boxes. If she put 4 strawberries into each box, there would be 3 strawberries left. If she put 6 strawberries into eah box, she would have 5 strawberries left.

If the no. of strawberries was between 100 and 150, how many strawberries did J buy?

I used the common multiple method but got many answers:

Common Multiple of 4, starting with 100 plus 3 excess:
103, 107, 111, 114, 119, 123, 127, 131, 135 etc

Common Multiple of 6, starting with 102 plus 5 excess:
107, 113, 119, 125, 131, 137

Why the answer is not 107 or 119 but 131? If this is not the correct method to apply, any other method?

[Superbugs]

Hi there, someone pls help me with the following questions:


Mdm Lek had 57 apples and oranges altogether. There were 3 fewer oranges than apples. Sh egave away half as many oranges as apples and was left with twice as many oranges as apples. How many apples did she give away?

I can only do up to here:
2U+3 => 57
1U=>27
Oranges =>27
Apples => 27+3 => 30

[Superbugs]

Pls help with this question too with other method other than guess and check:


Farmer Tan has ducsk and cows on his farm. The total number of ducks and cows is between 20 and 40. The ratio of the total no. of duck’s legs to the total no. of cow’s legs is 5:9. What is the total no. of ducks and cows on the farm?

Duck=> 2 legs
Cow=> 4 legs
Ratio of duck’s legs to cow’s leg
5:9
Since cow has 4 legs, I multiply the duck ratio by 2 to be on par with the cow legs, I get 10:9 => 19
Then guess and check method:
20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40
Since only 38 can be divisible by 19, the ans is 38.
Is this method correct?

Any other method?

[Dharma]

Total No. of Ducks = D

Total No. of Cows = C
Total no. of legs = 2D + 4C

Ratio of the no. of legs of ducks : no. of legs of cows = 2D : 4C = 5 : 9
18D = 20C
D : C = 20 : 18

Total no. of ducks and cows = 20 + 18 = 38