Math Problems: 1. The average of five number is 72....

[Derick]

I have a list of Problem sum & Fractions sum questions, needs help in solving these question: Please see below and share your working to the answer to these questions. Thanks a million!

1. The average of five number is 72. The average of the 5 number is 64 when one of the numbers is changed to 14. What is the original value of the changed number?

2. Melanie and Olivia have $2460. Oilivia and Johnathan have $692. Melanie has 9 times as much as Johnathan. How much does Olivia have?

3. A group of pupils took part in a competition. 1/3 of the boys and 1/6 of the girls were prize-winners. There are 35 prize-winners altogether and 4/7 of the prize-winners were boys. What is the fraction of the pupils were prize-winners. (Express your answer in simplest form)

4.Sam bought 5 games cartridge and 2 game console for $1440.50. Tone bought 8 games cartridge and 1 game console for $871.50. How much does each game cartridges and each game console?

5. Alison and Melvin saved $800.00 altogether. 1/4 of Alison's saving was $65.00 more than 1/5 of Melvin's saving. How much more money does Alison save than Melvin.

6. A cubic tank was filled completely with water. When 1/6 of the water from cubic tank was poured into a rectangle container, the container is 2/5 full. The capacity of the cubic tank was 125 litre more than that of the container.
(A) What is the volume of the water in the rectangle container?
(B) Given the rectangle container is 45cm long and 40cm wide, find the height of the water in the rectangle container.

 

[stapel]

I have a list of Problem sum & Fractions sum questions, needs help in solving these question: Please see below and share your working to the answer to these questions.

Actually, the "sharing your working" is what you are supposed to be doing! :shock:

1. The average of five number is 72. The average of the 5 number is 64 when one of the numbers is changed to 14. What is the original value of the changed number?

If the average is 72, then what is the sum? (Work backwards from the "average" formula.)

If the average is 64, then what is the sum?

By how much did the sum change?

If the new number is "14", then what was the old number?

2. Melanie and Olivia have $2460. Oilivia and Johnathan have $692. Melanie has 9 times as much as Johnathan. How much does Olivia have?

Then how much do nine of Johnathan and one of Olivia have? If you subtract one Olivia and one Johnathan, how much is left for eight Johnathans? Then how much does Johnathan have. Then how much does Olivia have?

3. A group of pupils took part in a competition. 1/3 of the boys and 1/6 of the girls were prize-winners. There are 35 prize-winners altogether and 4/7 of the prize-winners were boys. What is the fraction of the pupils were prize-winners. (Express your answer in simplest form)

How many prize-winners were boys?

Given that this number is one-third of the boys, how many boys are there?

How many prize-winners were girls?

Given that this number is one-sixth of the girls, how many girls are there?

So how many students are there?

Then what fraction were winners?

4.Sam bought 5 games cartridge and 2 game console for $1440.50. Tone bought 8 games cartridge and 1 game console for $871.50. How much does each game cartridges and each game console?

How much would Tone pay for 16 cartridges and 2 consoles?

Then what is the cost for 7 cartridges?

Then what is the cost for one cartridge?

Then what is the cost for one console?

5. Alison and Melvin saved $800.00 altogether. 1/4 of Alison's saving was $65.00 more than 1/5 of Melvin's saving. How much more money does Alison save than Melvin.

Melvin's savings is divided into five same-size chunks.

What is the value of Alison's savings, in terms of Melvin's chunks, plus money?

If you add these two, you get the whole $800.

If you subtract the money amount, what is the value of that number of Melvin's chunks?

Then what is the size of one of Melvin's chunks?

Then how much did Melvin save? How much did Alison save? What is the difference between these two values?

6. A cubic tank was filled completely with water. When 1/6 of the water from cubic tank was poured into a rectangle container, the container is 2/5 full. The capacity of the cubic tank was 125 litre more than that of the container.
(A) What is the volume of the water in the rectangle container?

One-sixth of the tank is two-fifths of the container. Then how much of the container's volume is equal to six-sixths of the tank's volume?

How much more than one tank-full is this?

Given that the overage is the 125 liters that the tank is larger than the container, how much is one-fifth of the container?

Then what is the capacity of the container? (You'll get fractions.)

(B) Given the rectangle container is 45cm long and 40cm wide, find the height of the water in the rectangle container.

What is the volume of the container, in liters? What then is the volume in milliliters?

What is the relationship between cubic centimeters, liters, and milliliters? What then is the volume in cubic centimeters?

Given the width and length, what then must be the height, in centimeters?

If you get stuck, please reply showing all of your work so far. Thank you!

 

[Derick]

Hi Stapel,

Below please find my working for the following questions

1. The average of five number is 72. The average of the 5 number is 64 when one of the numbers is changed to 14. What is the original value of the changed number?


72 x 5 = 360
64 x 5 = 320

360-320+(14) = 40+14 = 54 (answer)

Originally Posted by Derick
2. Melanie and Olivia have $2460. Oilivia and Johnathan have $692. Melanie has 9 times as much as Johnathan. How much does Olivia have?


I don't know how & where to start, please assist.

Originally Posted by Derick
3. A group of pupils took part in a competition. 1/3 of the boys and 1/6 of the girls were prize-winners. There are 35 prize-winners altogether and 4/7 of the prize-winners were boys. What is the fraction of the pupils were prize-winners. (Express your answer in simplest form)






How many prize-winners were boys?

35/1 x 4/7 = 20boys prize-winner

Given that this number is one-third of the boys, how many boys are there?

20x3=60 boys in total

How many prize-winners were girls?

35-20 = 15 girls prize-winner

Given that this number is one-sixth of the girls, how many girls are there?

15x6= 90 girls in total

So how many students are there?

90 girls + 60 boys = 150 students

Then what fraction were winners?

35/ 150 = 7/30 (answer)

 

[Derick]

Math Problems

Hi Stapel,

Thanks for the guide, i have managed to solve 1,3 4.

============================================================
But Q4, written guide, is this a typo error, it should read: "Then what is the cost for 11 cartridges instead of 7"

Originally Posted by Derick
4.Sam bought 5 games cartridge and 2 game console for $1440.50. Tone bought 8 games cartridge and 1 game console for $871.50. How much does each game cartridges and each game console?



How much would Tone pay for 16 cartridges and 2 consoles?

Then what is the cost for 7 cartridges?

Then what is the cost for one cartridge? ans: $27.50

Then what is the cost for one console? ans: $651.50

======================================================
Q2, 5, 6 - i am stuck. see below and advise, thanks!

Originally Posted by Derick
2. Melanie and Olivia have $2460. Oilivia and Johnathan have $692. Melanie has 9 times as much as Johnathan. How much does Olivia have?



Then how much do nine of Johnathan and one of Olivia have? If you subtract one Olivia and one Johnathan, how much is left for eight Johnathans? Then how much does Johnathan have. Then how much does Olivia have?

I have not manage to understand your guide, please assist to show me yr working, can? thanks!

Originally Posted by Derick
5. Alison and Melvin saved $800.00 altogether. 1/4 of Alison's saving was $65.00 more than 1/5 of Melvin's saving. How much more money does Alison save than Melvin.



Melvin's savings is divided into five same-size chunks.
What is the value of Alison's savings, in terms of Melvin's chunks, plus money?

4/4+(65x4)= Alison's saving
5/5=Melvin's saving
4/4+5/5+(260)=$800
40/20=$800-260
40/20=$540
1/20=$540/40
=13.50
(13.50x20)+260=Alison's saving = $530.00
(13.50x20) x 5 = Melvin's saving = $270.00

Ans: $260​

If you add these two, you get the whole $800.

If you subtract the money amount, what is the value of that number of Melvin's chunks?

Then what is the size of one of Melvin's chunks?

Then how much did Melvin save? How much did Alison save? What is the difference between these two values?

Originally Posted by Derick
6. A cubic tank was filled completely with water. When 1/6 of the water from cubic tank was poured into a rectangle container, the container is 2/5 full. The capacity of the cubic tank was 125 litre more than that of the container.
(A) What is the volume of the water in the rectangle container?



One-sixth of the tank is two-fifths of the container. Then how much of the container's volume is equal to six-sixths of the tank's volume?
6/6 = 12/5 = tank volume

How much more than one tank-full is this?

12-5 = 7 = 125 x12 = 1500 = 214 2
5 5 7 7 7

Given that the overage is the 125 liters that the tank is larger than the container, how much is one-fifth of the container?

Then what is the capacity of the container? (You'll get fractions.)

Originally Posted by Derick
(B) Given the rectangle container is 45cm long and 40cm wide, find the height of the water in the rectangle container.



What is the volume of the container, in liters? What then is the volume in milliliters?

12-5 = 7 = 125 x5 = 625 = 89 2
5 5 7 7 7

What is the relationship between cubic centimeters, liters, and milliliters? What then is the volume in cubic centimeters?
89 2 x 1000 = 625 x 1000 = 625000 milliliters divide 100 = 6250
7 7 7 7


Given the width and length, what then must be the height, in centimeters?


40cm x 45cm x H = 6250
7 (stuck ??)

 

[stapel]

2. Melanie and Olivia have $2460. Oilivia and Johnathan have $692. Melanie has 9 times as much as Johnathan. How much does Olivia have?

Then how much do nine of Johnathan and one of Olivia have? If you subtract one Olivia and one Johnathan, how much is left for eight Johnathans? Then how much does Johnathan have. Then how much does Olivia have?

I have not manage to understand your guide, please assist to show me yr working, can? thanks!

Try answering the first of the questions. If Melanie has nine times what Johnathan does, then what's another way of stating "nine of Johnathan"? Then how much is nine of Johnathan and one of Olivia? And so forth.

5. Alison and Melvin saved $800.00 altogether. 1/4 of Alison's saving was $65.00 more than 1/5 of Melvin's saving. How much more money does Alison save than Melvin.

Melvin's savings is divided into five same-size chunks.
What is the value of Alison's savings, in terms of Melvin's chunks, plus money?

4/4+(65x4)= Alison's saving
5/5=Melvin's saving
4/4+5/5+(260)=$800
40/20=$800-260
40/20=$540
1/20=$540/40
=13.50
(13.50x20)+260=Alison's saving = $530.00
(13.50x20) x 5 = Melvin's saving = $270.00

Ans: $260

Does this work out correctly? The values add to 800, so that part is right. What is one-fifth of Melvin's savings? What is one-fourth of Alison's savings? Is her one-fourth equal to Melvin's one-fifth, plus another sixty-five? If so, then your answer is correct.

6. A cubic tank was filled completely with water. When 1/6 of the water from cubic tank was poured into a rectangle container, the container is 2/5 full. The capacity of the cubic tank was 125 litre more than that of the container.
(A) What is the volume of the water in the rectangle container?

One-sixth of the tank is two-fifths of the container. Then how much of the container's volume is equal to six-sixths of the tank's volume?

6/6 = 12/5 = tank volume

How much more than one tank-full is this?

12-5 = 7 = 125 x12 = 1500 = 214 2
5 5 7 7 7

I don't know what you're doing here...?

(B) Given the rectangle container is 45cm long and 40cm wide, find the height of the water in the rectangle container.

What is the volume of the container, in liters? What then is the volume in milliliters?

12-5 = 7 = 125 x5 = 625 = 89 2
5 5 7 7 7

Same comment as above.