P6 Maths Question

[Worriedparent]

Hi, I recently came across a P6 maths question on a blog as follows:

Jack bought some pens and erasers for a total of $100.10. He spent $9.10 more on the pens than erasers. Each pen costs $3.70 more than each eraser. Jack bought 6 times more erasers than pens. How much does a pen cost?

The answer provided in the blog seems to suggest that there are 7 portions of erasers as compared to 1 portion of pens because "Jack bought 6 times more erasers than pens".

Now, I'm quite confused. Wouldn't "6 times more" mean there are 6 times more of one item as compared to another?? Why should there be 7 portions of erasers and 1 portion of pens??

Any views are appreciated. Thanks.

[stonston]

My answer for this question is $4.20 (Each pen costs $4.20.).

"Jack bought 6 times more erasers than pens."
Means that there are 6 units more erasers than pens.
Assuming that the number of pens is 1 unit, this means that erasers will be 6 units more, which means it is 7 units.
Ratio wise should be 1:7 (P:E).

This question is quite straightforward. It's a matter of understanding the question (the language usage).

[BbpHir3]

i agree with stonston

6 times more eraser than pens
meaning

- If there's 1 pen, the amt of eraser will be:
6 x 1 = 6
6 + 1 = 7 erasers

- If there's 2 pen, the amt of eraser will be:
6 x 2 = 12
12 + 2 = 14 erasers

so on and so forth....

by models,
it'll be something lyk this:

[Gladys]

Originally Posted by stonston My answer for this question is $4.20 (Each pen costs $4.20.). "Jack bought 6 times more erasers than pens." Means that there are 6 units more erasers than pens. Assuming that the number of pens is 1 unit, this means that erasers will be 6 units more, which means it is 7 units. Ratio wise should be 1:7 (P:E). This question is quite straightforward. It's a matter of understanding the question (the language usage).

I keep on trying but unable to get the answer of $4.20. Please help .thanks

[Daddy D]

Originally Posted by Gladys I keep on trying but unable to get the answer of $4.20. Please help .thanks

Err...
I think 6x7=42... somewhere along the line... just add the decimal points
Do they learn PE ratio in Pri 6?
If yes, then shld be ok to the kids.
If no, then shld be difficult.
But have to teach kids to be exam smart... if dont know... just proceed to do other problems... anyway it's only 1 question... still can get A grade

[Angelmum]

Originally Posted by Daddy D Err... ... anyway it's only 1 question... still can get A grade

Maths was my best subject but felt my O level questions easier than the P6 questions these days, now Maths std super high, I dont understand.
Later I go dig out some questions to 'test' experts here .... hehee

Skip one doesnt mean the rest will be straight fwd or easy nuts to crack, scarly end up goose egg!


btw, Stonston a Maths teacher?

[Daddy D]

Originally Posted by Angelmum Maths was my best subject but felt my O level questions easier than the P6 questions these days, now Maths std super high, I dont understand. Later I go dig out some questions to 'test' experts here .... hehee Skip one doesnt mean the rest will be straight fwd or easy nuts to crack, scarly end up goose egg! btw, Stonston a Maths teacher?

I also A student lehh... dont play play
Usually after doing the easy questions... warm up liaoo... then the difficult ones also not so difficult liaoo

[Angelmum]

1) Alex earned $450 more than Benny, Alex saved 3/4 of his salary while Benny saved 3/7 of his. Both spent the rest of their money. Benny's expenditure was twice as much as Alex's expenditure. Find the salary of Alex.

2) At 12 noon. Alan started from Town A travelling towards Town B at a uniform speed. One hr later, Betty started from Town B travelling towards Town A at a uniform speed 11 km/h slower than Alan's speed. They met each other on the way at 3pm. If the distance between Town A and Town B was 628 km, find Alan's speed?

3) Wendy bought CDs at $3 and sold them at $8 each. To promote sales, all customers who bought two CDs were given one free CD. After she had sold all the CDs, Wendy made a gain of $1235 despite giving away 150 CDs to ther custoemrs. How many of Wendy's customers bought only 1 CD?

4)


Is it I old, brain malfunction? How to do har?

[stonston]

To answer Angelmum's questions (I'm not sure if correct because I did not counter check my answers):
1) $3600
2) 130km/h
3) {WRONG! 127 customers} Correct = 37 Customers
4) 32cm2

[yumiao]

hmmm.... i dont't think it is correct
the salary should be 450x32/25, but lazy to really calculate how many. mind calculation.

[stonston]

Originally Posted by Angelmum 1) Alex earned $450 more than Benny, Alex saved 3/4 of his salary while Benny saved 3/7 of his. Both spent the rest of their money. Benny's expenditure was twice as much as Alex's expenditure. Find the salary of Alex.

This is how I solved the question (model method):
A = Alex
B = Benny
SP = Spent (Expenditure)
SA = Saved

A [_SP_][_SP_][_SA_][_SA_][_SA_][_SA_][_SA_][_SA_]
B [_SP_][_SP_][_SP_][_SP_][_SA_][_SA_][_SA_]


Benny spent TWICE as much as Alex (therefore Benny's expenditure is 4 units, Alex expenditure is 2 units).

Alex spent 1/4 of his pay. There for his pay is 8 units.
Benny spent 4/7 of his pay. There for his pay is 7 units.

Alex earned $450 more than Benny, which is 1 unit.
Alex's pay is 8 units:

1 unit -> $450
8 units -> $450 x 8 = $3600

[stonston]

Originally Posted by yumiao hmmm.... i dont't think it is correct the salary should be 450x32/25, but lazy to really calculate how many. mind calculation.

Just to counter check your answer:
450 x 32 / 25 = $576

That would mean:
A = $576
B = $126

A spent: $546/4 = $144
B spent: $144 x 2 = $288
{But he only earns $126, so how can he spend $288?}

[stonston]

Since now got abit of free time, I post my working for question 2 & 3.

2) At 12 noon. Alan started from Town A travelling towards Town B at a uniform speed. One hr later, Betty started from Town B travelling towards Town A at a uniform speed 11 km/h slower than Alan's speed. They met each other on the way at 3pm. If the distance between Town A and Town B was 628 km, find Alan's speed?

` Alan ->
` 12noon
` <------Distance travelled by Alan---->
A [________________________________/___________________________________________] B
```````````````````````````````` 3pm ````````````````````````````````````````` <- Betty
`````````````````````````````` Met Here ````````````````````````````````````````` 1pm
`````````````````````````````````` <---------------Distance Travelled by Betty------->` S = Alan's Speed - 11km/h
` <---------------------------Total Distance = 628km------------------------------------->

For every 1 hour, Alan will travel 11km MORE.
Alan travelled for 3 hours before they met (12noon to 3pm).
Better travelled for 2 hours before they met (1pm to 3pm).

By distance covered before they met:
A [_____][11km] x 3 hours } Total Distance
B [_____] x 2 hours } 628km

Therefore, total distance travelled by Alan & Betty is 5units + (11km x 3). This is also the distance of the entire journey.
Alan covered 3 units + (11km x 3), so:

5 units -> 628km - (11km x 3) = 595km
1 unit -> 119km
3 units -> 357km
357 km + 33 = 390km (Distance travelled by Alan)

Alan's Average Speed = Total Distance/Total Time = 390km/3hours = 130km/h



3) Wendy bought CDs at $3 and sold them at $8 each. To promote sales, all customers who bought two CDs were given one free CD. After she had sold all the CDs, Wendy made a gain of $1235 despite giving away 150 CDs to ther custoemrs. How many of Wendy's customers bought only 1 CD?

Assuming each CD was sold singly:
Profit per CD = $8 - $3 = $5

For every 1 CD Wendy gave away, she sold 2 CDs.
Therefore the profit for these CDs sold in bundle was:
$5 x 2 - $3 (cost of Free CD given away) = $7

She sold 150 of such bundles, so her earning from these bundles -> $7 x $150 = $1050

Her total profit was $1235.
Profit from CDs sold singly:
$1235 - $1050 = $185

Profit of each CD was $5, therefore:
$185/$5 = 37 CDs

37 customers bought only 1 CD.

[Angelmum]

Originally Posted by stonston Since now got abit of free time, I post my working for question 2 & 3.

Now I understand

[Gladys]

Originally Posted by stonston My answer for this question is $4.20 (Each pen costs $4.20.). "Jack bought 6 times more erasers than pens." Means that there are 6 units more erasers than pens. Assuming that the number of pens is 1 unit, this means that erasers will be 6 units more, which means it is 7 units. Ratio wise should be 1:7 (P:E). This question is quite straightforward. It's a matter of understanding the question (the language usage).

Hi Stonston,

Can you please show working for the above. Thank you.

[stonston]

Originally Posted by Gladys Hi Stonston, Can you please show working for the above. Thank you.

I lost the paper with my workings on it. Must wait till I'm more free to work it out again

[stonston]

I'm not sure if this is right, but based on my interpretation of the question:

Quantity of P:E is 1:7
P [__]
E [__][__][__][__][__][__][__]

Price of P & E (in total)
P [_______][_$9.10_] ``` } Total
E [_______] ``````````` }$100.10

By Price:
$100.10 - $9.10 = $91
2u -> $91
1 you -> $45.50

Since there are 7 units of erasers, each unit of erasers will cost $45.50/7 = $6.50

The price of the pens is $45.50 + $9.10 = $54.60

Price of pens take away the price of 1 unit of erasers (to find the difference in amount if the same amount of pens & erasers were bought):
$54.50 - $6.50 = $48.10

Since each pen is more expensive than each eraser by $3.70,
$48.10/$3.70 = 13 pens

To find the price of each pen:
$54.60/13pens = $4.20

[Gladys]

Originally Posted by stonston I'm not sure if this is right, but based on my interpretation of the question: Quantity of P:E is 1:7 P [__] E [__][__][__][__][__][__][__] Price of P & E (in total) P [_______][_$9.10_] ``` } Total E [_______] ``````````` }$100.10 By Price: $100.10 - $9.10 = $91 2u -> $91 1 you -> $45.50 Since there are 7 units of erasers, each unit of erasers will cost $45.50/7 = $6.50 The price of the pens is $45.50 + $9.10 = $54.60 Price of pens take away the price of 1 unit of erasers (to find the difference in amount if the same amount of pens & erasers were bought): $54.50 - $6.50 = $48.10 Since each pen is more expensive than each eraser by $3.70, $48.10/$3.70 = 13 pens To find the price of each pen: $54.60/13pens = $4.20

hi stonston,

thank you for taking your time to work out the working.

cheers

[yumiao]

Originally Posted by stonston Just to counter check your answer: 450 x 32 / 25 = $576 That would mean: A = $576 B = $126 A spent: $546/4 = $144 B spent: $144 x 2 = $288 {But he only earns $126, so how can he spend $288?}

Ya, you r right, the question is "Benny's expenditure was twice as much as Alex's expenditure". i didn't read carefully and do it in the way that "Alex's expenditure was twice as much as Benny's expenditure."

Conclusion, my brain is not big enough to put in all the drawing, better write on the picture. :P

[stonston]

Originally Posted by yumiao Ya, you are right, the question is "Benny's expenditure was twice as much as Alex's expenditure". i didn't read carefully and do it in the way that "Alex's expenditure was twice as much as Benny's expenditure." Conclusion, my brain is not big enough to put in all the drawing, better write on the picture. :P

No problem. Sometimes my brain can be abit dead also & never read the question properly

[pokemon97]

pls help me also...

1) Yesterday, a farm had a total of 1200 ducks and chickens. Today some chickens were sold and more ducks were brought into the farm. As a result, the number of ducks increased by 50% and the number of chickens decreased by 10%. There is now an equal number of ducks and chickens in the farm. Find the total number of chickens and ducks in the farm now.

[stonston]

Brain abit dead cos very late already. Had a long day at work.

Yesterday, a farm had a total of 1200 ducks and chickens. Today some chickens were sold and more ducks were brought into the farm. As a result, the number of ducks increased by 50% and the number of chickens decreased by 10%. There is now an equal number of ducks and chickens in the farm. Find the total number of chickens and ducks in the farm now.

Information Given:
At first
TOTAL C + D = 1200

Then
Some chicken were SOLD, - 10%
Some ducks were BOUGHT, + 50%
C = D

By model method:
C [_______________90% of C at first________________][--10% sold--]
D [______100% of D at first______][_50% of D at first_ ]

Comparing the percentages based on C:

Since D's 150% is same as C's 90%,
50% of D is the same as 30% of C.
Therefore D is converted into 60% and 30%:

C [_______________90% of C at first________________][--10% sold--]
D [______ 60% of D at first______][_ 30% of D at first_ ]

Total of C+D AT FIRST:
90% + 10% + 60% = 160%
160% = 1200 (total number of C+D at first)
1% = 7.5%

Total number of CHICKENS + DUCKS now:
180% = 1350 chickens & ducks


*********************************************
To counter check answers:

Total number of CHICKENS now:
90% = 675 chickens

Total number of DUCKS now:
90% = 675 ducks

If 10% of chickens were sold, there would be 750 chickens at first.
If 50% of the ducks were bought, there would be 450 ducks.

750 + 450 = 1200 (as given in question)

*********************************************

[yumiao]

Those who asking questions, are you the parents? You are facing problem how to teach your children? Haha, maybe the parents here can work together and orgnize a workshop for parents. How about that?

[stonston]

Originally Posted by yumiao Those who asking questions, are you the parents? You are facing problem how to teach your children? Haha, maybe the parents here can work together and orgnize a workshop for parents. How about that?

I've conducted workshops on challenging maths problems before. Response was overwhelming as my students' parents brought friends/relatives along! Too bad I dont't have time & classroom to do so now.

[pokemon97]

hi stonston, thanks for helping me to solve the question and with clear working. You are right, the answer is 1350