Q&A - PSLE Math

[MathIzzzFun]

Symum:

Hi,

Please help!
Lincoln spent $95 of his pocket every month and saved the rest. This month, he decided to spend only $75, thereby increasing his savings by 40%.
(a) What was his pocket money every month?
(b) Find the ratio of his expenditure to his savings for this month.

Thanks

Hi

Increase in savings --> $20
40% of savings --> $20
140% of savings --> $70

a) Pocket money = $75 + $70 = $ 145
b) ratio of expenditure to savings for this month = 75 : 70 = 15 : 14

cheers.

[MathIzzzFun]

Symum:

Hi,



Karen, Nora and Sakina baked a total of 280 tarts. Karen baked 1/4 as many tarts as Nora. Nora baked 4/5 as many tarts as Sakina. What percentage of the total number of tarts did Nora bake?


Thanks

Hi

Karen --> 1 unit
Nora --> 4 units
Sakina --> 5 units
Total 10 units

4/10 x 100% = 40%
Nora baked 40% of the tarts.

cheers.

[MathIzzzFun]

Symum:

Hi,



At city hall station, there were 360 commuters on an Mrt train. There were 20% more children than men and 20% fewer women than men on the train. 120 more commuters boarded the train at the next station. The number of women increased by 50% and the number of children increased by 25%. What was the percentage increase in the number of men?

Thanks

Hi

children : men --> 120 : 100 = 6 : 5
men : women --> 100 : 80 = 5: 4
children : men : women --> 6u : 5u : 4u
Total 15u --> 360, 1u --> 24
children --> 144
men --> 120
women --> 96
of 120 commuters boarded,
number of men boarded = 120 - 1/2 x 96 - 1/4 x 144 = 36
percentage increase in number of men = 36/120 x 100% = 30%

cheers.

[thinkgmama]

Hi,


Please help me with this question :

Samuel and Bob shared some stickers in the ratio 2:9.
The total number of stickers shared was between 120 and 170
After Bob had given some stickers to Samuel, the ratio became 3:4.
How many stickers did Bob have at first?

Thank you in advance.

[YumYum]

YumYum:

Hi, need help with this one as well: http://i43.tinypic.com/2wmi8hd.jpg\">

Dear MathIzzFun, thank you for your usual help.

[Zack7]

thinkgmama:

Hi,


Please help me with this question :

Samuel and Bob shared some stickers in the ratio 2:9.
The total number of stickers shared was between 120 and 170
After Bob had given some stickers to Samuel, the ratio became 3:4.
How many stickers did Bob have at first?

Thank you in advance.

before giving
S:B
2:9
total = 2+9 = 11 units

after giving
S:B
3:4 (* this ratio might be intended as 4:3, the question is a little vague)
total = 3+4 = 7 units

let the number of stickers given be x
let total be y

(9/11)y - (4/7)y = x ,

hence (19/77) y = x

this gives you the relationship between total stickers y against stickers given x.
that is, for every 77 total stickers, 19 stickers have to be given to maintain the ratios above

so the question says the total stickers is between 120 and 170, so assuming that stickers are whole numbers, 19/77 will be scaled by 2 to 38/154. remember that we are dealing with ratios, not absolute numbers.

this means for every 154 stickers, 38 have to be given to maintain the above ratios.

thus, 154 is the total stickers, and BOB had (9/11)y stickers in the beginning,
which means he has 126

[thinkgmama]

Zack7:

thinkgmama:

Hi,


Please help me with this question :

Samuel and Bob shared some stickers in the ratio 2:9.
The total number of stickers shared was between 120 and 170
After Bob had given some stickers to Samuel, the ratio became 3:4.
How many stickers did Bob have at first?

Thank you in advance.

before giving
S:B
2:9
total = 2+9 = 11 units

after giving
S:B
3:4 (* this ratio might be intended as 4:3, the question is a little vague)
total = 3+4 = 7 units

let the number of stickers given be x
let total be y

(9/11)y - (4/7)y = x ,

hence (19/77) y = x

this gives you the relationship between total stickers y against stickers given x.
that is, for every 77 total stickers, 19 stickers have to be given to maintain the ratios above

so the question says the total stickers is between 120 and 170, so assuming that stickers are whole numbers, 19/77 will be scaled by 2 to 38/154. remember that we are dealing with ratios, not absolute numbers.

this means for every 154 stickers, 38 have to be given to maintain the above ratios.

thus, 154 is the total stickers, and BOB had (9/11)y stickers in the beginning,
which means he has 126

Hi,

Thank you for the help rendered.


The part that I do not understand id why we have to scale it by 2. Is it because we have to meet the criteria of the 'total stickers is between 120 and 170'? Therefore if its not 19/77 but if it is ('40/120' - fictional) then there will be no need to scale?

This is the part which I do not understand. Can you help please? Thank you.

[tianzhu]

thinkgmama:

This is the part which I do not understand. Can you help please? Thank you.

Hi

One key point to take note is that the total number of stickers remains the same before and after the transfer.

Before
Samuel:Bob ------- 2:9(11) ------- 14:63 (77)

After
Samuel:Bob ------- 3:4 (7) -------- 33:44 (77)

Make the total number of units the same.A common multiple of 7 and 11 is 77.

The number of stickers is in multiples of 77

77,154,231.....

154 is between 120 and 170

77 units = 154

1 unit = 2

Bob = 63 units = 126

Best wishes

[MathIzzzFun]

thinkgmama:

Hi,


Please help me with this question :

Samuel and Bob shared some stickers in the ratio 2:9.
The total number of stickers shared was between 120 and 170
After Bob had given some stickers to Samuel, the ratio became 3:4.
How many stickers did Bob have at first?

Thank you in advance.

Hi
The transfer is between Samuel and Bob, so the total number of stickers will remain the same --> \"equalize\" the \"before\" and \"after\" ratios.

Before transfer:
Samuel : Bob --> 2:9 --> 14u : 63u (total 77u)
after transfer:
Samuel : Bob --> 3:4 --> 33u : 44u (total 77u)

Since the total number of stickers was between 120 & 170, the only multiple of 77 in this range is 77 x 2 = 154
So, 77u --> 154, 1u --> 2
At first, Bob --> 63u --> 126 stickers.

cheers.

[thinkgmama]

Thank you all of you. I finally understand appreciate the help.