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Math Help - Percentage problem

  1. #1
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    Percentage problem

    In the first quarter of the year, Jean spent 72% of her salary. In the next 4 months, she saved 25% more than what she saved in the first quarter of the year. If Jean's monthly salary of $1800 remained the same through out the year, what was her average monthly expenditure for the first seven months?

    I did this question about four times and I keep on getting $1314 but the book says the answer is $1224. Could someone help me on this?


    Sue wanted to cut a piece of ribbon into two smaller pieces. At first ,she wanted the first piece of ribbon to be 210cm long. Then she changed her mind and decided to reduce it by 20cm. This would increase the length of the second piece by 8%. What was the total length of the whole piece of ribbon before Sue cut it?

    If 20 cm = 8%
    then 10 cm = 4 %
    250 cm = 100%

    then this makes the second piece 250 cm plus 190cm should be 440cm but the book says the answer is 460cm . Did I do something wrong?



    Two sisters, Mary and Julia shared $72. When their mother gave them another $10 each, Julia has 16% less money than Mary. What is the ratio of the amount of Mary's money to Julia's money at first?

    Mary - Julia =16% of 92
    I tried to sovle it this way but it didn't work.
    Is the equation wrong?
    I am trying to stop using guessing and checking to get the answers.

    Vicky.


    Thanks
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  2. #2
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    Quote Originally Posted by Vicky1997 View Post
    In the first quarter of the year, Jean spent 72% of her salary. In the next 4 months, she saved 25% more than what she saved in the first quarter of the year. If Jean's monthly salary of $1800 remained the same through out the year, what was her average monthly expenditure for the first seven months?

    I did this question about four times and I keep on getting $1314 but the book says the answer is $1224. Could someone help me on this?
    The answer is indeed $1224.

    So for the first three months, she spent 72% of her salary, which means she spent .72*1800 = $1296 each month for the first three.

    But now we need to know how much she spent per month for the last 4 months.

    The clue here is that she SAVED 25% more per month, so now we have to ask, how much did she save per month for the first three?

    The answer is 1800-1296 = $504

    Now we know she saved 25% more than that, which comes out to be 1.25*504 = $630

    Which means she SPENT 1800 - 630 = $1170 per month for the last 4 months


    So now we get that the average is: (3*1296 + 4*1170)/7 = $1224
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  3. #3
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    Quote Originally Posted by Vicky1997 View Post
    Sue wanted to cut a piece of ribbon into two smaller pieces. At first ,she wanted the first piece of ribbon to be 210cm long. Then she changed her mind and decided to reduce it by 20cm. This would increase the length of the second piece by 8%. What was the total length of the whole piece of ribbon before Sue cut it?

    If 20 cm = 8%
    then 10 cm = 4 %
    250 cm = 100%

    then this makes the second piece 250 cm plus 190cm should be 440cm but the book says the answer is 460cm . Did I do something wrong?
    Unfortunately, you did do something wrong. Although these are pretty weird percentage problems...

    Anyway, she's cutting a ribbon up into two pieces. Let's say that the total length is l and that the length of the second piece is p

    When she decided to make the first piece 20cm shorter, that means she decided to make the second piece length ( p) 20cm LONGER (which increased the size of the second piece by 8%).

    So that means that: 1.08p = p+20
    So: .08p = 20
    So: p=20/.08=250cm

    So the second piece, BEFORE adding the 20 cm is 250.

    So the total length is 210+250 = 460cm
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  4. #4
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    Quote Originally Posted by Vicky1997 View Post
    Two sisters, Mary and Julia shared $72. When their mother gave them another $10 each, Julia has 16% less money than Mary. What is the ratio of the amount of Mary's money to Julia's money at first?

    Mary - Julia =16% of 92
    I tried to sovle it this way but it didn't work.
    Is the equation wrong?
    I am trying to stop using guessing and checking to get the answers.
    For this one, I will just start you off in the right direction.

    Let's say Mary's original amount of money (before getting $10 more) is: M

    And Julia's is: J

    We know two equations. (Note that 1-.16 = .84)

    M+J=72
    J+10=.84(M+10)
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  5. #5
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    Thanks for your help. I really appreciate it.

    Vicky.
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