Tutor MathsGuru: Ask me for your burning Maths questions!

[jieheng]

Jcong:

Please help me.


Beaker A and Beaker B contained 9 litres of water altogether at first. Jamie poured 1/3 of the water from Beaker A to Beaker B. Next she poured 3/8 of the water from Beaker B to Beaker A. She then had the same volume of water in the 2 beakers. How much water was there in each beaker at first? Express your answer in ml.

Thanks for your help.

To solve this type of question , we need to count backwards .

A [------------------]

B [------------------]

Jamie poured 3/8 of the water from Beaker B to Beaker A ,

the volume of water remained in breaker B is 5/8

A [--][--][--][--][--]

B [--][--][--][--][--]

Transferred back 3u (3/8 of B) from A to B

A [--][--]

B [--][--][--][--][--][--][--][--]

Jamie poured 1/3 of the water from Beaker A to Beaker B

A left 2u as 1u was poured to B

Transferred back 1u from B to A

A [--][--][--] (3u)

B [--][--][--][--][--][--][--] (7u)

9 litres = 9000 ml

total 10u -----> 9000
1u ------> 900

the amount of water in breaker A at first = 3u = 3*900 = 2700 ml (Ans)

the amount of water in breaker B at first = 7u = 7*900 = 6300 ml (Ans)

[charken]

hi mathsguru,

1st question

I have a very tough question for you.Matthew used 1/5 of a box of sugar
for cooking and 3/4 of the remainder to make bread.The rest were packed
equally into 5 packets.what fraction of the total amount of sugar was in each packet?
2nd question
Serene filled up7/8 of her petrol tank for a trip .She used 6/11of the petrol by the end of the trip.The capacity of her petrol tank was 70literes.
how much did she use for the trip.
express the answer as a decimal correct to 1 decimal place.
(only for this question.)
ths

[jieheng]

charken:

hi mathsguru,

1st question

I have a very tough question for you.Matthew used 1/5 of a box of sugar
for cooking and 3/4 of the remainder to make bread.The rest were packed
equally into 5 packets.what fraction of the total amount of sugar was in each packet?
2nd question
Serene filled up7/8 of her petrol tank for a trip .She used 6/11of the petrol by the end of the trip.The capacity of her petrol tank was 70literes.
how much did she use for the trip.
express the answer as a decimal correct to 1 decimal place.
(only for this question.)
ths

Q1)

[-----][-----][-----][-----][-----]

[-----] for cooking

[-----][-----][-----] for making bread

[-----] -----> 1/5

The fraction of the total amount of sugar was in each packet = (1/5) / 5 = 1/25 (Ans)

Q2)

the amount of petrol in 7/8 of the petrol tank = ( 7/8 ) * 70 = 61.25

the amount of petrol she used for the trip was = ( 6/11 ) * 61.25 = 33.4 litres (Ans)

[jieheng]

Vanilla Cake:

Pls help to solve the following Maths sums:



Question 29
Sn where S is the sum of the digits of n.
Example: S1 -> S=1 and S29 -> S=2+9=11
What is the sum of S1+S2+S3+.......S2010+S2011?
(6 marks)

Note:
Sn-> n is a subscript
S1-> 1 is a subscript
S2-> 2 is a subscript
S3-> 3 is a subscript
S29-> 29 is a subscript
S2010-> 2010 is a subscript
S2011-> 2011 is a subscript

Thanks in advance for your time and effort to provide the worked solutions.

Sum of S1 to S9 = (1+2+3+4+5+6+7+8+9) = 45

Sum of S10 to S19 = Sum of all ten-digits + Sum of all one-digits = 1*10 + 45

Sum of S20 to S29 = Sum of all ten-digits + Sum of all one-digits = 2*10 + 45

Sum of S1 to S99 = (1+2+3+4+5+6+7+8+9)*10 + 45*10 = 450 + 450 =900

S100 = 1

Sum of S101 to S199 = Sum of all hundred-digits + 900 = 1*99 + 900

S200 = 2

Sum of S201 to S299 = Sum of all hundred-digits + 900 = 2*99 + 900

Sum of S1 to S999 = (1+2+3+4+5+6+7+8+9)*99 + 900*10 + (S100+S200+.......................+S900) = 45*99 + 900*10 + 45 = 13500

S1000 = 1

Sum of S1001 to S1999 = 1*999 + 13500

Sum of S1 to S1999 = 13500 + 1 + 1*999 + 13500 = 28000

S2000 = 2

Sum of S2001 to S2011 = 2*11 + (1+2+.....+9) + 1 + 2 = 25 + 45 = 70

Sum of S1 to S2011 = 28000 + 2 + 70 = 28072 (Ans)

[Jcong]

John has 993 tables and chairs at first. After he sold 2/5 of the tables and 5/8 of the chairs, he had 459 tables and chairs left. How many tables did he sell?

[jieheng]

Jcong:

John has 993 tables and chairs at first. After he sold 2/5 of the tables and 5/8 of the chairs, he had 459 tables and chairs left. How many tables did he sell?

Note : There is no direct relationship between 1 unit of table and 1 unit of chair
T [---][---][---][---][---] = (5[---])

C [*][*][*][*][*][*][*][*] = (8[*])

5[---] + 8[*] -----> 993

T [---][---][---] = (3[---])

C [*][*][*] = (3[*])

3[---] + 3[*] -----> 459

1[---] + 1[*] -----> 459/3 = 153

8[---] + 8[*] -----> 153*8 = 1224

3[---] + 5[---] + 8[*] -----> 1224

3[---] + 993 -----> 1224

3[---] -----> (1224 - 993) = 231

1[---] -----> 231/3 = 77

2[---] -----> 77*2 = 154

Number of tables that he sold = 154 (Ans)

[wahwah]

Hi jieheng,

Thanks for the solution, but can explain some of the workings? Thanks!

4. Mr Tan bought three times as many badges as toy cars ad spent $144 in total. He spent $84 more on toy cars than on badges. given that a toy car costs $10.40 more than a badge, what is the cost of a badge?

B [-----][-----][-----]

C [-----]

cost of the badges = (144 - 84) / 2 = 30
Why divide by 2?

[jieheng]

wahwah:

Hi jieheng,

Thanks for the solution, but can explain some of the workings? Thanks!

4. Mr Tan bought three times as many badges as toy cars ad spent $144 in total. He spent $84 more on toy cars than on badges. given that a toy car costs $10.40 more than a badge, what is the cost of a badge?

B [-----][-----][-----]

C [-----]

cost of the badges = (144 - 84) / 2 = 30
Why divide by 2?

Hi wahwah ,

You are welcome.

Cost of the toy cars = Cost of the badges + $84 (He spent $84 more on toy cars than on badges)

Cost of the badges + Cost of the toy cars = $144

Cost of the badges + Cost of the badges + $84 = $144

2 * Cost of the badges = $144 - $84 = $60

Cost of the badges = $60 / 2 = $30

[wahwah]

Hi jieheng,

Thanks for the detailed explanation.
Sorry to trouble you again. Can you explain the working for this question?

2. Wayne had five more 50cents coins than 20cents coins. After he used eight 50cents coins, the value of 50cents coins is $1.50 more than the value of 20cents coins. How many coins did he have at first?


50cents [------][ 3][5]
20cents [-----][3]

value of [3] = 3 * 0.2 = $0.60

the difference in value between [------] and [-----] = 1.5 + 0.6 = 2.1
What are we trying to find here?

the difference in value of one coin between 50 cents and 20 cents = $0.30

number of coins in [------] = 2.1 / 0.3 = 7

Total number of coins he had at first =( 7 + 3 ) * 2 + 5 = 25 (Ans
How to get (7+3)*2+5?

[jieheng]

wahwah:

Hi jieheng,

Thanks for the detailed explanation.
Sorry to trouble you again. Can you explain the working for this question?

2. Wayne had five more 50cents coins than 20cents coins. After he used eight 50cents coins, the value of 50cents coins is $1.50 more than the value of 20cents coins. How many coins did he have at first?


50cents [------][ 3][5]
20cents [-----][3]

value of [3] = 3 * 0.2 = $0.60

the difference in value between [------] and [-----] = 1.5 + 0.6 = 2.1
What are we trying to find here?

the difference in value of one coin between 50 cents and 20 cents = $0.30

number of coins in [------] = 2.1 / 0.3 = 7 ,


Total number of coins he had at first =( 7 + 3 ) * 2 + 5 = 25 (Ans
How to get (7+3)*2+5?

At first ,

number of coins in [------] = 2.1 / 0.3 = 7 ,

number of coins in [-----] = 7

the number of 50-cents coins he had = [------][ 3][5] = 7 + 3 + 5

the number of 20-cents coins he had = [-----][3] = 7 + 3

total number of coins he had at first =(7 + 3 + 5) + 7 + 3 = =( 7 + 3 ) * 2 + 5 = 25