Q&A - P5 Math

[jieheng]

shann2:

Some ratio questions... Please help. TIA


The ratio of the number of pens to the number of erasers in a shop was 5 : 1. When 10 pens were sold and the shopkeeper bought 10 more erasers, there is twice as many pens as erasers. How many more pens than erasers were there in the shop in the end?

At first
Pens 5u
Erasers 1u
Total 6u

After 10 pens were sold and the shopkeeper bought 10 more erasers , total no of pens and erasers remained the same .

In the end
Pens 2u ------------>Pens 4u
Erasers 1u --------->Erasers 2u
Total 3u ------------>Total 6u

5u - 4u = 1u

1u --> 10

Pens 4u , Erasers 2u

Different = 4u - 2u = 2u = 2*10 = 20

[smartmummy]

shann2:

Some ratio questions... Please help. TIA


The ratio of the number of pens to the number of erasers in a shop was 5 : 1. When 10 pens were sold and the shopkeeper bought 10 more erasers, there is twice as many pens as erasers. How many more pens than erasers were there in the shop in the end?

Concept: External changed quantity
P:E
5:1 [5U:1U]
-10 +10
2:1 [2P:1P]
Make the parts equal
5U-10=2U+20
3U=30
1U=10
1P=1U+10=20
There were 20 more pens than erasers in the end

[Jamesbond]

smartmummy:

shann2:

Some ratio questions... Please help. TIA


In a ballroom, the ratio of the number of dancers to the number of non-dancers is 7 : 5. The ratio of the number of male dancers to the number of female dancers is 8 : 3. If 4/5 of the non-dancers are women and there are 56 male dancers, how many men and women are there in the ballroom?

D:ND
7:5
MD:FD
8:3
MD=56
8u=56
1u=7
3u=21
D=MD+FD=56+21=77
7P=77 [I use P as the 1P is different from 1U]
P=11
5P=55
D+ND=77+55=132
There are 132 men and women in the Ballroom

Hi smartmummy, can u pl let me know why is 7P=77...

[smartmummy]

Jamesbond:

smartmummy:

[quote=\"shann2\"]Some ratio questions... Please help. TIA


In a ballroom, the ratio of the number of dancers to the number of non-dancers is 7 : 5. The ratio of the number of male dancers to the number of female dancers is 8 : 3. If 4/5 of the non-dancers are women and there are 56 male dancers, how many men and women are there in the ballroom?

D:ND
7:5
MD:FD
8:3
MD=56
8u=56
1u=7
3u=21
D=MD+FD=56+21=77
7P=77 [I use P as the 1P is different from 1U]
P=11
5P=55
D+ND=77+55=132
There are 132 men and women in the Ballroom

Hi smartmummy, can u pl let me know why is 7P=77...[/quote]
cos D:ND-----7:5
number of dancers is 77 that is equal to 7 units

[iCreative Math]

shann2:

Some ratio questions... Please help. TIA


The ratio of the number of pens to the number of erasers in a shop was 5 : 1. When 10 pens were sold and the shopkeeper bought 10 more erasers, there is twice as many pens as erasers. How many more pens than erasers were there in the shop in the end?

Hi Shann2, one more method for your child to consider ....

The question tells us that the shopkeeper now has twice as many pens as erasers. We further know that this is after the shopkeeper has bought 10 more erasers. We therefore start off the problem-solving as follows:-

\"NOW\" Position: (i.e. after selling 10 pens and buying 10 erasers)

Pens: ( 2 units + 20 )
Erasers: ( 1 unit + 10 )

\"AT FIRST\" Position: (i.e. before selling 10 pens and buying 10 erasers),

Pens: ( 2 units + 20 + 10 )
Erasers: ( 1 unit )

The question further tells us that the ratio of pens to erasers was 5 : 1 AT FIRST.

hence, we can deduce that:-

5 units = 2 units + 30

3 units = 30

1 unit = 10

Hence, the shopkeeper NOW has

(2 units + 20) or 40 pens; and (1 unit + 10) or 20 erasers.

The shoppers has 20 more pens than erasers in the end.


I hope your child will find this method simpler.


Best Regards,
iCreative Math

[shann2]

Thank you iCreative Math, smartmummy & speedmaths.com .

I understood your solutions!
Really appreciate the help. Thanks!

[cimman]

shann2:

The ratio of the number of pens to the number of erasers in a shop was 5 : 1. When 10 pens were sold and the shopkeeper bought 10 more erasers, there is twice as many pens as erasers. How many more pens than erasers were there in the shop in the end?

here is an approach using Table Heuristics.
1st Step: draw the table:
http://i42.tinypic.com/1675kxz.png\">

2nd Step: Transfer all values from the problem sum to the table. As we read from the 1st sentence to the last sentence of the problem sum, we transfer the values.
http://i41.tinypic.com/ix4fmp.png\">

3rd Step: fill in the blank boxes and circle the relevant equations.
Then we write out the answer in terms of the relevant variables and proceed to solve the equations.
All Transfer type problems follow this equation:
Before + Transfer = After
http://i39.tinypic.com/bzvyh.png\">

here's a What If scenario.
What if the Transfer does not involve -10, +10 (Unchanged Total Concept)? then we don't need to fill up the Total column. We still have Equation 3 and Equation 2.
http://i41.tinypic.com/e7xn2u.png\">
Equation 1 is not really necessary. It just makes solving the equations a little easier.
Recognizing the Unchange Total Concept is a bonus to solving the equations, but it is not critical if one is familiar with solving simultaneous equations.
The 2u=p equation is managed through equalizing the Units and Parts approach, so one does not have to deal with simultaneous equations, though in the above example, I've used another approach.

Regardless of the type of Transfer Problem and regardless of the values in the problem sums, the above 3 steps are used in all problems in the Table Heuristics approach.

[Jamesbond]

Thank you smartmummy.

[swordtail]

Jane paid $75 for 25 similar pencils and 12 similar files. Mary paid $23.30 for 6 such pencils and 5 such files. Find the total cost of each pencil and each file.


tks

[Oldschool]

swordtail:

Jane paid $75 for 25 similar pencils and 12 similar files. Mary paid $23.30 for 6 such pencils and 5 such files. Find the total cost of each pencil and each file.


tks

Hi,

For primary, one way is to ‘Make Supposition’.

Suppose Jane buys same number of files

$75 x 5 = $375 for 125 pens and 60 files
$23.3 x 12 = $279.6 for 72 pens and 60 files

125 pens – 72 pens = 53 pens
$375 – $279.6 = $95.4

53 pens will cost $95.4
1 pen will cost $1.8

You can continue with “Suppose Jane buys same number of pens” to find the cost of 1 file or make use of one of the conditions above. I’ll use the 2nd condition here,

$23.3 for 6 pens and 5 files
6 pens cost $10.8
5 files cost ($23.3 - $10.8) = $12.5
1 file cost $2.5

Total cost of 1 pen and 1 file = $1.8 + $2.5 = $4.3

Regards