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Math Help - help mi wif tis new questions

  1. #1
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    wooow.. thxz.. how about tis question?
    Attached Thumbnails Attached Thumbnails help mi wif tis new questions-gash.jpg  
    Last edited by CaptainBlack; June 23rd 2006 at 11:15 AM.
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  2. #2
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    (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
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  3. #3
    MHF Contributor Quick's Avatar
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    Quote 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%


    Quote 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.
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  4. #4
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    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.

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  5. #5
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    nono.. (b)ii the ans is yes. had the money been shared 4 yrs ago. Mary would have recevied $12000x 8/16.... $9600~~???
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  6. #6
    MHF Contributor Quick's Avatar
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    Quote 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).
    Quote 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.
    Quote 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}
    Last edited by Quick; June 24th 2006 at 07:46 AM.
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