help mi wif tis new questions

**xiaoz** · June 23rd 2006, 10:30 AM

wooow.. thxz.. how about tis question?

**Jameson** · June 23rd 2006, 11:06 AM

(a)Start with the students who scored from 0-50 marks, inclusive. "x students scored less than 51 marks". So x students represents all the marks from 0-50. Now go to the students who made from 50-100 marks, inclusive. "2x students scored more than 49 marks". So 2x students represents all the marks from 50-100. We've counted the number of students who have scored 50 marks twice though, so we need to make note of the info the problem gave and subtract out one of these times we double counted.

So total number of students: $x+(2x-6)$

And we also know that the total number of students is: $16$

$x+2x-6=18$

$x=\frac{24}{3}=8$

**Quick** · June 23rd 2006, 01:52 PM

Originally Posted by some boring school assignment

Mr. Wang decided to give his grandchildren, Peter and Mary, $12,000. This sum is to be divided between them in the ratio of their ages. The children's mother suggested that the money should be invested to allow it to grow for a few years before being shared out. After 4 years, Peter, aged 6, received his share of $4,800 and Mary, aged 12, received $9600.
$(\text{i})$ Express the growth of money as a percentage of the original sum of $12,000.

First things first, find out how much money was there when they were finished investing. Peter got 4,800 and Mary got 9600. Together they got $4800+9600=14400$
Now you need to find out how much more money you have, $14400-12000=2400$
Now to find the percent increase, you need to divide the amount of money gained by the amount you started out with $2400\div12000=0.2$ which equals 20%

Originally Posted by some boring school assignment

$(\text{ii})$ Mary said, "There is no growth in my share at all." Do you agree with Mary? Give a numerical example to support your opinion.

What you need to do is find out what she is comparing. She is comparing the share she would've gotten without the investment to the share she is getting after the investment. Now we need to figure out what her share was before the money was invested... and to do that, we need to find Peter and Mary's Ages at that time (4 years ago)

$\text{Peter's Age 4 Years Ago}=$ $\text{Peter's Age}-4\rightarrow P=6-4\rightarrow P=2$

$\text{Mary's Age 4 Years Ago}=$ $\text{Mary's Age}-4\rightarrow M=12-4\rightarrow M=8$

Now we must find how much mary would have gotten, which means we have to divide Mary's age by peter's and Mary's ages added together

$\frac{M}{M+P}=\frac{8}{8+2}=\frac{8}{10}=0.8$

Now we multiply 12000 by 0.8 to get Mary's share

$12000 \times 0.8 = 9600$

So mary was right, her share didn't change.

**Soroban** · June 23rd 2006, 02:19 PM

Hello, xiaoz!

I did part (ii) differently . . . same punchline.

Mr. Wang decided to give his grandchildren, Peter and Mary, $12,000.
This sum is to be divided between them in the ratio of their ages.
The children's mother suggested that the money should be invested
to allow it to grow for a few years before being shared out.
After 4 years, Peter, aged 6, received his share of $4,800 and Mary, aged 12, received $9600.

(ii) Mary said, "There is no growth in my share at all." .Do you agree with Mary?

Four years ago, Peter was $2$ years old and Mary was $8$ .

The ratio of their ages is: $2:8 = 1:4$ .
The $\$12,000$ would have been divided in the ratio: $\frac{1}{5} : \frac{4}{5}$
Peter would have received: $\frac{1}{5}\times\$12,000 \,=\,\$2,400$
Mary would have received: $\frac{4}{5}\times\$12,000 \,=\,\boxed{\$9,600}$

Four years later, the money has grown to $\$4,800 + 9,600 \,= \,\$14,400.$

Peter is $6$ years old and Mary is $12$ .

The ratio of their ages is: $6:12 = 1:2$

The $\$14,400$ is divided in the ratio: $\frac{1}{3}:\frac{2}{3}$
Peter received: $\frac{1}{3} \times \$14,400\,=\,\$4,800$
Mary received: $\frac{2}{3} \times \$14,400\,=\,\boxed{\$9,600}$

I agree . . . Mary's share did not increase.

**xiaoz** · June 24th 2006, 06:58 AM

nono.. (b)ii the ans is yes. had the money been shared 4 yrs ago. Mary would have recevied $12000x 8/16.... $9600~~???

**Quick** · June 24th 2006, 07:33 AM

Originally Posted by xiaoz

nono.. (b)ii the ans is yes. had the money been shared 4 yrs ago. Mary would have recevied $12000x 8/16.... $9600~~???

Both me and soroban have said the answer is yes (remember, yes means marry was right).

Originally Posted by Quick

$\frac{M}{M+P}=\frac{8}{8+2}=\frac{8}{10}=0.8$

Now we multiply 12000 by 0.8 to get Mary's share

$12000 \times 0.8 = 9600$

So mary was right, her share didn't change.

Originally Posted by Soroban

The ratio of their ages is: $2:8 = 1:4$ .
The $\$12,000$ would have been divided in the ratio: $\frac{1}{5} : \frac{4}{5}$
Peter would have received: $\frac{1}{5}\times\$12,000 \,=\,\$2,400$
Mary would have received: $\frac{4}{5}\times\$12,000 \,=\,\boxed{\$9,600}$

---------

I agree . . . Mary's share did not increase.

note: $\frac{8}{10}=\frac{4}{5}$

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