Q&A - PSLE Math

[Dharma]

Hifive:

Hello everyone


HAPPY NEW YEAR!

I've a question:

Peter, Queenie, Regina and Sally saved $1030. The ratio of Peter's money to Queenie's money was 1 : 2. Peter took 2/5 of Regina's money. He then gave $95 from the amount taken from Regina to Sally. Finally, the 3 girls had the same amount of money.

a) How much did Regina have at first ?
b) How much did Sally have in the end?

Appreciate your advice.

At first, their share
Peter : 3u
Queenie : 6u
Regina : 6u + 4u = 10u
Sally : 6u - $95

25u - $95 = $1030
25u = $1125
1u = $45

a) Amt Regina had at first = 10u = $450
b) Amt Sally had in the end = 6u = $270

[Hifive]

Hi Dharma


Good morning! Thanks for the solution.

Can you pls advise on how do you derive that Peter : 3u and Queenie : 6u?

Thanks!

[Dharma]

Hifive:

Hi Dharma


Good morning! Thanks for the solution.

Can you pls advise on how do you derive that Peter : 3u and Queenie : 6u?

Thanks!

The final condition is :

The 3 girls had the same amount of money( I assumed 6u for each of the 3 girls).
Notice that Queenie's money did not change at all. So, Queenie had 6u at the beginning too.
Since the qn tells us that ratio of money Peter to Queenie at first is 1:2.
Therefore, Peter must have had 3u at first.

[Lynn2]

May I know anyone here can share where can I find very challenging questions for Circles?thanks


Rgds
Lynn

[Belle2011]

Dear everybody,

Happy New Year to you.

Here is another question from a worksheet given by a teacher from Just Education.

Karen is about as many days as her mother is in weeks and Karen is as months as her grandpa is in years. Karen, her mother and her grandpa are 160 years old altogether. How old is her grandpa?
(model answer: 96)

My problem is I dont really understand some parts in this question and thus unable to solve.

Thanks.

Cheers,
Belle.

[Dharma]

Belle2011:

Dear everybody,

Happy New Year to you.

Here is another question from a worksheet given by a teacher from Just Education.

Karen is about as many days as her mother is in weeks and Karen is as months as her grandpa is in years. Karen, her mother and her grandpa are 160 years old altogether. How old is her grandpa?
(model answer: 96)

My problem is I dont really understand some parts in this question and thus unable to solve.

Thanks.

Cheers,
Belle.

Karen : Mother = a days : a weeks = a/7 weeks : a weeks = 1 : 7
Karen : Grandpa = b months : b years = b/12 years : b years = 1 : 12

Karen : Mother : Grandpa : 1 : 7 : 12
1u + 7u + 12u = 160
20u = 160
1u = 8

Grandpa's age = 12u = 12 x 8 = 96 years old

[Belle2011]

Dharma:

Belle2011:

Dear everybody,

Happy New Year to you.

Here is another question from a worksheet given by a teacher from Just Education.

Karen is about as many days as her mother is in weeks and Karen is as months as her grandpa is in years. Karen, her mother and her grandpa are 160 years old altogether. How old is her grandpa?
(model answer: 96)

My problem is I dont really understand some parts in this question and thus unable to solve.

Thanks.

Cheers,
Belle.

Karen : Mother = a days : a weeks = a/7 weeks : a weeks = 1 : 7
Karen : Grandpa = b months : b years = b/12 years : b years = 1 : 12

Karen : Mother : Grandpa : 1 : 7 : 12
1u + 7u + 12u = 160
20u = 160
1u = 8

Grandpa's age = 12u = 12 x 8 = 96 years old

Dear Dharma,
Thanks very much for your prompt reply.

May I ask:
why consider weeks for Karen: Mother?
why consider years for Karen: Grandpa?
Also,
when you combine the 3 persons ie Karen: Mother: Grandpa, can we simply lump the ratios since Karen: Mother is originally in weeks and Karen: Grandpa is originally in years, if you know what I mean?
Thanking you in advance.

Cheers,
Belle.

[Hifive]

Dharma:

The final condition is :

The 3 girls had the same amount of money( I assumed 6u for each of the 3 girls).
Notice that Queenie's money did not change at all. So, Queenie had 6u at the beginning too.
Since the qn tells us that ratio of money Peter to Queenie at first is 1:2.
Therefore, Peter must have had 3u at first.

Hi Dharma

Thanks. I can understand now.

[tianzhu]

Belle2011:

May I ask:
why consider weeks for Karen: Mother?
why consider years for Karen: Grandpa?

Hi Belle2011

Good Morning

Another way to look at it to use the number of days as the basis of comparison.

The ratio of Karen’s age to her mother is 1:7 (7 days in a week)

The ratio of Karen’s age to her grandpa is 1:12 (12 months in a year)

Ratios is a comparison of two or more quantities of the same kind, so we convert the months and weeks into number of days.

Therefore, the ratio of Karen’s age to her grandpa is 28:336 (we assume that 1 week --- 7 days, 1 month --- 4 weeks)
Use equivalent ratios to reduce to the lowest term, we have 1:12

So the ratios (in the form of days)
Karen:mother --- 1:7
Karen:grandpa --- 1:12

Karen:mother:grandpa --- 1:7:12

1u+7u+12u --- 160 (Total age is 160)

20u --- 160
1u --- 8

12u ---8*12 --- 96 (grandpa’s age)

Best wishes

[Belle2011]

Dear tianzhu,

Once again, thanks very much for your solution.

Cheers,
Belle.