Q&A - P5 Math

[Udon]

Need help...thanks


Q1. The height of the water level in a tank rose from 80 cm to 1.16 m. Express the increase in the height of the water level as a percentage of the original height of the water level.

How to calculate the original height?


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....

[verykiasumummy]

Udon:

Need help...thanks


Q1. The height of the water level in a tank rose from 80 cm to 1.16 m. Express the increase in the height of the water level as a percentage of the original height of the water level.

How to calculate the original height?


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....

hi udon,

Q1. the original height need not be calculated, already in the question stated 80cm was the original height.
so take 116cm - 80cm = 36cm.

36/80 x 100% = 45%

Q2.
Peter : 30mins to clean the car
30mins --> 1 car
5mins --> 1/6 of the car.

Bro : 15mins to clean the car.
15mins --> 1 car
5mins --> 1/3 of the car.

so in 5 mins, both of them will clean
1/6 + 1/3 = 3/6 (1/2 of the car)

so 5 x 2 = 10mins.
(in 10mins, they will clean the whole car together)

[usaik]

Hi,


Anyone can help to solve the following without the use of algebra please? Thank you.

There were a total of 540 blue and red balls in a truck. 1/3 of the blue balls and 1/5 of the red balls were removed from the truck . After that a total of 388 balls were left in the truck. Find the ratio of the number of blue balls to the number of red balls in the truck at first.

[cimman]

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.

Mr Chen bought some pencil cases and bags for the children at a gathering. The price of each pencil case was $2.40 while the price of each bag was $10.80. For every 4 bag bought, he was given one such pencil case for free. After receiving the free pencil cases, the number of pencil cases was 1/3 of the number of bags bought. If Mr Chen paid a total of $1584, how much more did he pay for the bags than the pencil cases ?

this is an interesting problem. It is a Unit Value and Ratio problem. It is a unit value problem because it has the concept of unit value ie. each pencil case was $2.40...., and it has the ratio concept ie. for every...
That in itself is not the interesting part. The interesting part is that it is a 2 level ratio problem. The majority of ratio problems are single level, ie. Tom's Apple to Jane's Apple. In this case, a second level relationship was introduced, ie. Paid / Free. The second level is linked to the first level, ie. Pencil Case. Treat this concept like the Classification topic in Science.
http://i46.tinypic.com/qqq0ec.png\">
The above table was drawn to illustrate how the ratios are derived. You can simplify it to this table:
http://i45.tinypic.com/sbt3ia.png\">
A common ratio technique is used to equalize the ratios so that u=p.
Next, we plug the quantity values into the table below:
http://i47.tinypic.com/auxyg.png\">

An alternative solution using modelling:
http://i48.tinypic.com/19sdo1.png\">
However, some children might not be able to derive the model so easily. The table approach is easier if the meaning of the ratio components are clearly understood. You will notice that the solution is independent of the numerical values, ie. it is not dependent on numbers being nice multiples.

If you treat this problem as a 2 step problem, it will be easier to analyze.
The first step was to derive the value of Paid Pencil Cases Quantity.
The second step was to derive the relationship between the Total Cost of Paid Pencil Cases and Bags.
Paid Pencil Case is the component we need to find, and not Free Pencil Case because it has a Unit Value of 2.40. The free pencil case would have a unit value of 0.

[MathIzzzFun]

Xiao Hu:

lotto:

[quote=\"KP2\"]

Hi KP2,

If this is the question that u mean,

[i]Mr Chen bought some pencil cases and bags for the children at a gathering. The price of each pencil case was $2.40 while the price of each bag was $10.80. For every 4 bags bought, he was given one such pencil case for free. After receiving the free pencil cases, the number of pencil cases was 1/3 of the number of bags bought.
If Mr Chen paid a total of $1584, how much more did he pay for the bags
than the pencil

The answer key is wrong I think :scratchhead:
Hope mine is correct and can be understood.
But it is way too messy :imsorry:
I'm still not use to post solution here



Thx Lotto ! Ur answer is the same as the answer key .

Your welcome.
Why is mine wrong... Grrr :mad:

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.[/quote]

Hi

cimman has provided a detailed solution.

For this question, the student needs to understand that the total number of pencil cases comprised of purchased ones and FOC ones. So, the key is to determine how many pencil cases were bought and how many were given free with the purchase of the bags.

From the final ratio of bags : pencil cases = 3 : 1 = 12u : 4u, we can determine the number of pencil cases given FOC & purchased from the first given ratio ie for every 4 bags purchased, 1 pencil case was given free...

From final ratio --> 12u of bags purchased --> 12u/4 = 3u of pencil cases were given FOC.

Therefore, number of pencil cases purchased = 4u-3u = 1u

which means
number of pencil case purchased : bags purchased
= 1u : 12u
... with this, it should be quite easy to determine the number of pencil cases and bags purchased using value x quantity method or grouping concept.

cheers.

[MathIzzzFun]

usaik:

Hi,


Anyone can help to solve the following without the use of algebra please? Thank you.

There were a total of 540 blue and red balls in a truck. 1/3 of the blue balls and 1/5 of the red balls were removed from the truck . After that a total of 388 balls were left in the truck. Find the ratio of the number of blue balls to the number of red balls in the truck at first.

http://i48.tinypic.com/5feous.png\">

cheers.

[MathIzzzFun]

aps:

Hi all


I need help to solve this qn urgently. Thanks in advance.

John always gives 20% of what he earns to his father. In March, his father received $185 less than in February. In April, his father received $165.75 more than in March. If John's percentage decrease in earning from February to March was the same as the percentage increase from March to April, how much did he earn in April?

pls confim the value in blue..

cheers.

[aps]

MathIzzzFun:

aps:

Hi all


I need help to solve this qn urgently. Thanks in advance.

John always gives 20% of what he earns to his father. In March, his father received $185 less than in February. In April, his father received $165.75 more than in March. If John's percentage decrease in earning from February to March was the same as the percentage increase from March to April, how much did he earn in April?

pls confim the value in blue..

cheers.

Hi MathIzzzFun

It is $195.

Thanks!

[MathIzzzFun]

aps:

Hi all


I need help to solve this qn urgently. Thanks in advance.

John always gives 20% of what he earns to his father. In March, his father received $195 less than in February. In April, his father received $165.75 more than in March. If John's percentage decrease in earning from February to March was the same as the percentage increase from March to April, how much did he earn in April?

Thanks!

Hi

The allowance is reduced/increased by the same percentage as the reduction/increase in salary.

http://i49.tinypic.com/20jidjc.png\">

http://i50.tinypic.com/28v7k2q.png\">

cheers.

[aps]

Hey MathIzzzFun


You are a genius! Thanks so much for helping! :rahrah: