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  1. #1
    Member Sazza's Avatar
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    Please Reada::...

    Hey, i've decided to give myself some things to work out., in preparation for my Exam. Obviously it's not any questions from the exam, how would i have got a hold of them? They may seem easy, but some people do happen to be Dyslexic:
    I originally posted this in another forum, but they obviously didnít get what I mean: I posted that this was NOT homework. I had set myself a question to answer, and i wanted to find out HOW!
    People immediately presume, that every question that resembles these ones must be homework =[


    Peter works as a real estate agent and is paid commission at a variable rate. He receives 4% on the first $100 000 of sales, 21/2 % on the next $100 000 of sales and 11/2% on the remaining balance of sales. If peter sellís a house for $349 000 how much will he be paid?


    Monica knows that the selling price of a walkman is $89.95. She also knows that this price includes a mark up of 10%. What was the original price of the walk-man?
    (Potentially you would go like this if it was not a mark up) 89.95 x 10% (without having to use the =ís sign)


    And: The Numbers in the left column have been changed to the numbers in the right column. Determine the percentage change and state whether it was an increase or decrease.

    3452 ----- 4315
    6060 ------- 2908.8
    I have already established that both have been increased? But Iím not sure about these percentage changes =[


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  2. #2
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    6060 to 2908.8 is an increase? are you sure about that one?
    if you want to figure out the percentage change from one thing to another
    \frac{x}{100} = \frac{4315}{3452} cross multiply and if you are looking for the ("50% more" or what not just subtract 100% from that)
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  3. #3
    Member Sazza's Avatar
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    Oops, i mean't de-crease!
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  4. #4
    Member Sazza's Avatar
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    I don't get what you mean!
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  5. #5
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    ok ill show you,
    \frac{x}{100} = \frac{4315}{3452}
    now you can multiply across the equals sign, following the principles of algebra
    3452x =  100 \cdot  4315
    so now we divide by 3452
    x = \frac{100 \cdot 4315}{3452}
    punch it into our handy dandy calculator (or google it)
    so x is 125! that means 4315 is 125% of 3452 or equivalently
    4315 is 25% more than 3452
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  6. #6
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    well ok and to your other problems, well im not sure i get the first one so soundly, but for the second one what you want to know is what number + 10% = 89.95

    what youre really saying is that 110% of x (the original cost is equal to 89.95
    well so convert the 110% to decimal and you have the equation
    1.1x = 89.95
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  7. #7
    Member Sazza's Avatar
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    Quote Originally Posted by Ilaggoodly View Post
    ok ill show you,
    \frac{x}{100} = \frac{4315}{3452}
    now you can multiply across the equals sign, following the principles of algebra
    3452x = 100 \cdot 4315
    so now we divide by 3452
    x = \frac{100 \cdot 4315}{3452}
    punch it into our handy dandy calculator (or google it)
    so x is 125! that means 4315 is 125% of 3452 or equivalently
    4315 is 25% more than 3452


    Thanks alot =]
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  8. #8
    Member Sazza's Avatar
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    Quote Originally Posted by Ilaggoodly View Post
    ok ill show you,
    \frac{x}{100} = \frac{4315}{3452}
    now you can multiply across the equals sign, following the principles of algebra
    3452x = 100 \cdot 4315
    so now we divide by 3452
    x = \frac{100 \cdot 4315}{3452}
    punch it into our handy dandy calculator (or google it)
    so x is 125! that means 4315 is 125% of 3452 or equivalently
    4315 is 25% more than 3452
    Quote Originally Posted by Ilaggoodly View Post
    well ok and to your other problems, well im not sure i get the first one so soundly, but for the second one what you want to know is what number + 10% = 89.95

    what youre really saying is that 110% of x (the original cost is equal to 89.95
    well so convert the 110% to decimal and you have the equation
    1.1x = 89.95


    Erm, but 89.95 wasn't the original size! What would be a basic way of doing it on the calculator?
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  9. #9
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    youre right, 89.95 isnt, x is the original size
    divide by 1.1
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  10. #10
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    Hello, Sazza!

    Peter works as a real estate agent and is paid commission at a variable rate.
    He receives 4% on the first $100,000 of sales, 2Ĺ% on the next $100,000 of sales
    and 1Ĺ% on the remaining balance of sales.
    If Peter sells a house for $349,000, how much will he be paid?
    Peter gets 4% of the first $100,000: . 0.04 \times 100,000 \:=\:4,000

    He gets 2Ĺ% of the next $100,000: . 0.025 \times 100,000 \:=\:2,500

    And he gets 1Ĺ% of the rest: . 0.015 \times 149,000 \:=\: 2,235

    His total commission is: . \$4,000 + 2,500 + 2,235 \;=\;\$8,735



    Monica knows that the selling price of a Walkman is $89.95.
    She also knows that this price includes a mark up of 10% (of cost).
    What was the original cost of the Walkman?
    We know that: . \text{Cost} + \text{Markup} \;=\;\text{Selling price} .[1]

    . . We also know that: . \text{Markup} \;=\;10\%\text{ of Cost}

    Substitute into [1]: . \text{Cost} + \text{(10\% of Cost)} \;=\;\text{Selling price}

    Then: . \text{(100\% of Cost)} + \text{(10\% of Cost)} \;=\;\text{Selling price}

    . . So we have: . \text{110\% of Cost} \;=\;\text{Selling price}\quad\Rightarrow\quad 1.10C \:=\:S


    Since S = 89.95, we have: . 1.10C = 89.95

    . . Then: . C \:=\:\frac{89.95}{1.10} \:=\:81.7727...


    Therefore, the original cost was about \$81.77.



    The Numbers in the left column have been changed to the numbers in the right column.
    Determine the percentage change and state whether it was an increase or decrease.

    \begin{array}{cc}3452  & 4315 \\ 6060 & 2908.8 \end{array}
    The first one changed from 3452 to 4315. .There was an increase of 863
    . . Percent of increase: . \frac{863}{3452} \:=\:0.25 \;=\;25\%

    The second one changed from 6060 to 2908.8. .There was a decrease of 3151.2
    . . Percent of decrease: . \frac{3151.2}{6060} \;=\;0.52 \;=\;52\%

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