Tutor MathsGuru: Ask me for your burning Maths questions!

[Jcong]

A container of red dye weighs 2.27 kg when it is 1/3 full. Another identical container of red dye weighs 4.8 kg when it is 6/7 full. What is the weight of the empty container?

[YumYum]

MathIzzzFun:

YumYum:

Hi,


I have some Qns which I need some help with. My son is still struggling with the method to use. I bought \"Challenging Maths Problems Made Easy\" by Ammiel Wan, though he can do the Qns from the book, he struggles when it comes to those from past papers. Any advice on how to tackle this *big* problem? :?

1. Mary, Omar and AiLing shared $4590 amongst themselves. Omar and Ailing shared 4/9 of the money equally. After Omar gave away some of his money to Mary, Ailing had 3 times as much money as Omar. How much money did Omar give to Mary?

2. Alice & Gillian had a total of $555. Alice spent 5/6 of her money and Gillian spent 2/9 of her money. In the end, the amount of money Gillian had left was 7 times the amount of money Alice had left.

(a) how much money did Alice spend?

(b) What was the total amount of money left?

3. The ratio of the number of pencils to the number of erasers in a box is 7:3. When 36 pencils are removed and 24 erasers are added, there is an equal number of pencils and erasers. How many pencils are there in the box in the end?

4. Gary and Jane shared the cost of a dinner in the ratio of 2:3. Gary used half of his money to pay for his share. After paying fo her share, Jane had $84 left. The ratio of the amount of money that Gary had at first to the amount of money Jane had at first was 3:4. How much was the total bill for the dinner?


5. 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?

many thanks

Hi

Q4.
The ratio of the amount of money that Gary had at first to the amount of money Jane had at first = 3:4 = 12u : 16u

Gary and Jane shared the cost of a dinner in the ratio of 2:3 = 6u : 9u

Comparing the ratios, amount of money Jane had left = 16u - 9u = 7u

7u = $84 => 1u = $12

Cost of dinner = 6u + 9u = 15u = 15 x $12 = $180

Q5.
Number of goldfish more than swordtails = 1/17 x 204 = 12

After same number of goldfish and swordtails were sold, there were still 12 more goldfish than swordtails.

Since the remaining number of goldfish and swordtails were in the ratio of 9 : 5 ie 9u : 5u

4u = 12 => 1u = 3

Total number of goldfish and swordtails left = 9u+5u = 14u = 14 x 3 = 42

So total number of goldfish and swordtails giiven away = 204 - 42 = 162

cheers.

Dear MathIzzzFun,

Thank you for taking your time at the early hr of the morning to reply to the Qns. Let me go thru' and also pass these to my son and we'll check with you again if we need some additional help. *pie-seh*.

:lol:

[MathIzzzFun]

YumYum:

MathIzzzFun:

[quote=\"YumYum\"]Hi,


I have some Qns which I need some help with. My son is still struggling with the method to use. I bought \"Challenging Maths Problems Made Easy\" by Ammiel Wan, though he can do the Qns from the book, he struggles when it comes to those from past papers. Any advice on how to tackle this *big* problem? :?

1. Mary, Omar and AiLing shared $4590 amongst themselves. Omar and Ailing shared 4/9 of the money equally. After Omar gave away some of his money to Mary, Ailing had 3 times as much money as Omar. How much money did Omar give to Mary?

2. Alice & Gillian had a total of $555. Alice spent 5/6 of her money and Gillian spent 2/9 of her money. In the end, the amount of money Gillian had left was 7 times the amount of money Alice had left.

(a) how much money did Alice spend?

(b) What was the total amount of money left?

3. The ratio of the number of pencils to the number of erasers in a box is 7:3. When 36 pencils are removed and 24 erasers are added, there is an equal number of pencils and erasers. How many pencils are there in the box in the end?

4. Gary and Jane shared the cost of a dinner in the ratio of 2:3. Gary used half of his money to pay for his share. After paying fo her share, Jane had $84 left. The ratio of the amount of money that Gary had at first to the amount of money Jane had at first was 3:4. How much was the total bill for the dinner?


5. 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?

many thanks

Hi

Q4.
The ratio of the amount of money that Gary had at first to the amount of money Jane had at first = 3:4 = 12u : 16u

Gary and Jane shared the cost of a dinner in the ratio of 2:3 = 6u : 9u

Comparing the ratios, amount of money Jane had left = 16u - 9u = 7u

7u = $84 => 1u = $12

Cost of dinner = 6u + 9u = 15u = 15 x $12 = $180

Q5.
Number of goldfish more than swordtails = 1/17 x 204 = 12

After same number of goldfish and swordtails were sold, there were still 12 more goldfish than swordtails.

Since the remaining number of goldfish and swordtails were in the ratio of 9 : 5 ie 9u : 5u

4u = 12 => 1u = 3

Total number of goldfish and swordtails left = 9u+5u = 14u = 14 x 3 = 42

So total number of goldfish and swordtails giiven away = 204 - 42 = 162

cheers.

Dear MathIzzzFun,

Thank you for taking your time at the early hr of the morning to reply to the Qns. Let me go thru' and also pass these to my son and we'll check with you again if we need some additional help. *pie-seh*.

:lol:[/quote]
Most glad to help :lol:

cheers.

[YumYum]

HappyFaye:

Ok, let me try again.


In this case, 'Broken' Model is used as we do not know how many units/boxes to draw.

First construct a 'broken' model of a multiple of 10 with 15 left

When each children were given 12 marbles, it is the same as each child is getting another 2 more marbles. We can then construct another 'broken' model of a multiple of 4 + multiple of 2 with 1 left.

So 15 - 1 = 14 marbles.

Since 14 marbles were given to the number of children of 2 more marbles each,
14 marbles / 2 --> 7

So 7 children have 2 more marbles each.

So there are 7 children.

If each child has 10 marbles, total marbles --> (10 x 7) + 15 = 85
The answer is the same if each child has 12 marbles.

Hope this is not too confusing, without the broken models drawn here.

Thank you for the detailed explanation. Sorry, what is \"broken model\"? I just got hold of the book \"Challenging Maths Made Easy\" to educate myself on the various Maths techniques, still gropping in the dark...

Can I check on why we need to divide 14/2, a bit lost here... thks

[jieheng]

Jcong:

A container of red dye weighs 2.27 kg when it is 1/3 full. Another identical container of red dye weighs 4.8 kg when it is 6/7 full. What is the weight of the empty container?

1/3 -----> 7/21

6/7 -----> 18/21

the capacity of the container is 21u

weight of empty container + 7u -----> 2.27 [when the contaner is 7/21 (1/3) full]


weight of empty container + 18u -----> 4.8 [when the contaner is 18/21 (6/7) full]

weight of empty container + 7u + 11u -----> 4.8

2.27 + 11u -----> 4.8

11u -----> (4.8 - 2.27) = 2.53

1u -----> 2.53 / 11 = 0.23

weight of empty container + 7u -----> 2.27

weight of empty container + 7*0.23 -----> 2.27

weight of empty container -----> (2.27 - 1.61) = 0.66 kg (Ans)

[MathIzzzFun]

YumYum:

HappyFaye:

Ok, let me try again.


In this case, 'Broken' Model is used as we do not know how many units/boxes to draw.

First construct a 'broken' model of a multiple of 10 with 15 left

When each children were given 12 marbles, it is the same as each child is getting another 2 more marbles. We can then construct another 'broken' model of a multiple of 4 + multiple of 2 with 1 left.

So 15 - 1 = 14 marbles.

Since 14 marbles were given to the number of children of 2 more marbles each,
14 marbles / 2 --> 7

So 7 children have 2 more marbles each.

So there are 7 children.

If each child has 10 marbles, total marbles --> (10 x 7) + 15 = 85
The answer is the same if each child has 12 marbles.

Hope this is not too confusing, without the broken models drawn here.

Thank you for the detailed explanation. Sorry, what is \"broken model\"? I just got hold of the book \"Challenging Maths Made Easy\" to educate myself on the various Maths techniques, still gropping in the dark...

Can I check on why we need to divide 14/2, a bit lost here... thks

Hi YumYum,


The key here is to work on the additional marbles that each child gets and the number of marbles left over.

\"If each child were given 10 marbles, there would be 15 marbles left over.\" >> Every child gets 10 marbles, 15 left over.

\"If each child were given 12 marbles, there would be 1 marble left over. \" >> Every child gets 2 more marbles, 1 left over.

So, the question can be rephrased as :\"I have 15 marbles. If I were to give each child 2 marbles, I will have one marble left. How many children are there ?\"

>> number of marbles given = 15 -1 =14. Each child gets 2 marbles more, number of children = 14 /2 = 7

cheers.

[CJM]

Mrs ho used a total of 5/6 kg of sugar in march and April. She used 7/12kg more sugar in march than in April. How much sugar did she use in April?

[CJM]

Mr Goh is 3 times as old as his daughter who is 12 years old. What will be their total age in 13 year’s time?

[Daddy]

Hi,


Need help on the question.

Jason, Kelvin and Lily had a total of 161 stamps at first. Jason gave away 1/5 of his stamp. Kelvin received 34 more stamps. Lily bought some more stamps and hence tripled her original number of stamps. Then, the ratio of the number of stamps Jason, Kelvin and Lily had was 2:3:6. How many stamps did Kelvin have at first.


Thanks.
Daddy

[jieheng]

CJM:

Mrs ho used a total of 5/6 kg of sugar in march and April. She used 7/12kg more sugar in march than in April. How much sugar did she use in April?

March + April = 5/6

March + March + 7/12 = 10/12

March = (3/12) / 2 = 3/24

April = March + 7/12 = 3/24 + 7/12 = 3/24 + 14/24 = 17/24 kg (Ans)