Q&A - P5 Math

[bookwormkids]

Please help!


Q1
There were 920 seats in a concert. The last four rows were priced 70% of the rest of the seats. There were 55 seats each in the last four rows. The total amount collected when all the seats were sold was $25 620. How much was the cost of each seat in the back row?

Q2
The average number of stickers of Paul, Quinn, Roy and Steve is 75. The ratio of the total number of stickers of Paul and Quinn to the ratio of the total number of stickers of Roy and Steve is 7 : 3. The number of Roy’s stickers is 1/4 the number of Steve’s stickers. What is the average number of stickers of Paul, Quinn and Roy?

Q3
A basket of pears were divided among Alice, Betty and Clara. Alice received 6 more than 1/4 of the pears. Betty received 4 more than 1/3 of the remaining pears. Clara received half of the remainder, plus the last 3 pears. What percentage of the pears did Clara receive? (round off your answer to 2 decimal place)

Thank you!

[MathIzzzFun]

bookwormkids:

Please help!


Q3
A basket of pears were divided among Alice, Betty and Clara. Alice received 6 more than 1/4 of the pears. Betty received 4 more than 1/3 of the remaining pears. Clara received half of the remainder, plus the last 3 pears. What percentage of the pears did Clara receive? (round off your answer to 2 decimal place)

Thank you!

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cheers.

[MathIzzzFun]

bookwormkids:

Please help!


Q2
The average number of stickers of Paul, Quinn, Roy and Steve is 75. The ratio of the total number of stickers of Paul and Quinn to the ratio of the total number of stickers of Roy and Steve is 7 : 3. The number of Roy's stickers is 1/4 the number of Steve's stickers. What is the average number of stickers of Paul, Quinn and Roy?


Thank you!

Total number of stickers --> 75 x 4 = 300

Paul & Quinn's stickers : Roy & Steve's stickers
= 7 : 3
= 210 : 90

Roy' stickers : Steve's stickers = 1 : 4
Roy's stickers --> 1/5 x 90 = 18

Total number of stickers for Paul, Quinn & Roy = 210 + 18 = 228

Average number of stickers of Paul, Quinn & Roy = 228/3 = 76

cheers.

[MathIzzzFun]

bookwormkids:

Please help!


Q1
There were 920 seats in a concert. The last four rows were priced 70% of the rest of the seats. There were 55 seats each in the last four rows. The total amount collected when all the seats were sold was $25 620. How much was the cost of each seat in the back row?

Thank you!

Price of a seat, not in last 4 rows --> 1u
Price of a seat in last 4 rows --> 0.7u

Total number of seats in last 4 rows --> 55 x 4 = 220
Total amount collected for seats in last 4 rows = 220 x 0.7u = 154u

Total number of seats in other rows = 920-220=700
total amount collected for seats in other rows = 700 x 1u = 700u

Total amount collected for all seats = 700u + 154u = 854u

854u --> $ 25620
1u --> $30

Cost of a seat in back row = 0.7 x $30 = $21

cheers.

[bookwormkids]

Hi MathIzzzFun! Thank you so much! shall pass the solutions to my kid to digest them !

[lotto]

Xiao Hu:

Hi Lotto,
Looks like you are assuming the number of bags bought are multiples of 4. Can it not be multiples of 4? If say, number of bags bought is 6, then free pencil case is 2. So he may have bought 1 more pencil case, then ratio of pencil case to bag is 2/6 = 1/3, which is what the end ratio is. But the starting ratio is not 1/4 (1 free pencil case to 6 bags).

I don't know how to solve it in any other way though.

May be gurus like Tianzhu and MathIzzzzFun can help us here?

Thanks,
Xiaohu.

Hi Xiao Hu,

In Maths, our brain is automatically thinking that it must be a multiple of 4 when we read the question (especially for primary school).

If you are looking into that type of answer, u might need to do 4 workings (for multiple of 4, multiple of 4 +1, multiple of 4 +2, multiple of 4 +3) and check one by one and end up with 4 solutions too.

Take it easy! It is not as hard as u think.

Cheers :celebrate:

[Udon]

MathIzzzFun:

Udon:

Need help...thanks


Q2. Peter took 30 minutes to clean his father's car while his elder brother only took 15 minutes to clean it. How long would both of them take to clean the car together?

It's Average calculation method right? I tried to add and divide but still could not find the answer....

Two alternate approaches for such questions:

1) Find LCM of 15 and 30 --> 30
Suppose cleaning the car represents 30 units of work.

Then,
Peter's work rate --> 30 units/ 30 min = 1 unit/min
Elder brother's work rate --> 30 units/ 15 min = 2 units/ min

when both clean the car together,
combined work rate --> 2 units/min + 1 unit/min = 3 units/min

and time taken to clean the car together = 30 units ÷ 3 units/ min = 10 min

2) In 30 min,
Peter would clean 30/30 = 1 car
Elder brother would clean 30/15 = 2 cars

So, they would clean 3 cars together in 30 min
To clean 1 car together, time taken = 30 min/3 = 10 min

cheers

Thank you so much....

[YumYum]

Hi, can someone pls help with this Qn:


Aaron and Ben shared a sum of $200. Aaron gave 3/5 of what he has to Ben. Ben later gave 1/5 of what he has back to Aaron. They ended up with equal amount of money. How much did Aaron have at first? Thanks.

[verykiasumummy]

YumYum:

Hi, can someone pls help with this Qn:


Aaron and Ben shared a sum of $200. Aaron gave 3/5 of what he has to Ben. Ben later gave 1/5 of what he has back to Aaron. They ended up with equal amount of money. How much did Aaron have at first? Thanks.

hi, offering my help :

i would use working backwards method.. note that this is internal transfer and constant total.

They ended up with equal amount of money.
so $200 / 2 = $100

Ben later gave 1/5 of what he has back to Aaron.
means Ben would have 4/5 left and this 4/5 is $100.
4/5 --> $100
1/5 --> $25 (Ben gave back to Aaron)
5/5 --> $125 (Ben has $125 after Aaron gave him 3/5 of his money)

$200 - $125 = $75 (Since Ben has $125 after receiving money from Aaron, Aaron should have $75 left after giving his money to Ben.)

Aaron gave 3/5 of what he has to Ben.
so Aaron should have 2/5 of money left.
2/5 --> $75
1/5 --> $37.50
5/5 --> $187.50 (Aaron had at first)

$200 - $187.50 = $12.50 (Ben had at first)

[YumYum]

Verykiasummummy: thanks!