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Math Help - Help with this word problem!

  1. #1
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    Help with this word problem!

    Hi guys can you please help me with this question.

    The value of a new car of a particular make, A, decreases by 22.5% during the first year. In the second year, its value decreases by 12.5% of its value at the beginning of the year. The value of a new car of another make, B, decreases by 25% during the first year. In the second year, its value decreases by 15% of its value at the beginning of the year. A new car of make A costs $48,000 and a new car of make B costs $42,000.

    (a) What is the difference between the values of the two cars at the end of the firts year? Express this differnce as a percentage of the value of the car of make A at the end of the first year.

    (b) Calculate the difference between the values of the two cars at the end of the second year.

    Thankyou!
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  2. #2
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    Quote Originally Posted by laser2302
    Hi guys can you please help me with this question.

    The value of a new car of a particular make, A, decreases by 22.5% during the first year. In the second year, its value decreases by 12.5% of its value at the beginning of the year. The value of a new car of another make, B, decreases by 25% during the first year. In the second year, its value decreases by 15% of its value at the beginning of the year. A new car of make A costs $48,000 and a new car of make B costs $42,000.

    (a) What is the difference between the values of the two cars at the end of the firts year? Express this differnce as a percentage of the value of the car of make A at the end of the first year.

    (b) Calculate the difference between the values of the two cars at the end of the second year.

    Thankyou!
    If something decreases by 22.5% means it is worth 77.5% perfect of the original price.
    In the beggining the car was worth x after the first year is it .775x after the second year it decreases by 12.5% meaning its value is 87.5% of the new price thus,
    .875(.775x)=.678125x
    Similarily the second car after two years is,
    .85(.75x)=.6375x and .75x after one year.

    The first problem asks for the difference after the first year.
    The first car is worth .775\times 48,000=37,200. The second car is worth .75\times 42,000=31,500 The difference is,
    37,200-31,500=5,700

    After two years, you have the new values,
    .875\times 37,200=32,250
    .85\times 31,500=26,775
    Their difference is,
    32,250-26,775= 5475
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  3. #3
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    Quote Originally Posted by ThePerfectHacker
    The first problem asks for the difference after the first year.
    The first car is worth .775\times 48,000=37,200. The second car is worth .75\times 42,000=31,500 The difference is,
    37,200-31,500=5,700
    The question asks to write this out in terms of the percentage of the price of car A, so you divide 5,700 by the price of car A

    \frac{5700}{37200}=0.153225806\approx\boxed{15<br />
\text<br />
{percent}}
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  4. #4
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    Hello, laser2302!

    Are you sure you can't work this out yourself?


    [quote]The value of a new car of a particular make, A, decreases by 22.5% during the first year.
    In the second year, its value decreases by 12.5% of its value at the beginning of the year.

    The value of a new car of another make, B, decreases by 25% during the first year.
    In the second year, its value decreases by 15% of its value at the beginning of the year.

    A new car of make A costs $48,000 and a new car of make B costs $42,000.

    (a) What is the difference between the values of the two cars at the end of the first year?
    Express this differnce as a percentage of the value of the car of make A at the end of the first year.

    (b) Calculate the difference between the values of the two cars at the end of the second year.

    During year 1, make A loses 22.5\%\text{ of }\$48,000 \:=\:0.225 \times 48,000 \:=\:\$10,800
    . . . At the end of year 1, it is worth only: \$48,000 - 10,800 \:= \:\$37,200

    During the year 2 A loses 12.5\%\text{ of }\$37,200 \:=\:0.125 \times 37,200 \:= \:\$4,650
    . . . At the end of year 2, it is worth only: \$37,200 - 4,650\:=\:\$32,550


    During year 1, make B loses 25\%\text{ of }\$42,000\:=\:0.25 \times 42,000 \:=\:\$10,500
    . . . At the end of year 1, it is worth only: \$42,000 - 10,500\:=\:\$31,500

    During year 2, B loses 15\%\text{ of }\$31,500 \:=\:0.15 \times 31,500\:=\:\$4,725
    . . . At the end of year 2, it is worth only: \$31,500 - 4,725\:=\:\$26,775


    Now that we've worked all the numbers, we can answer the questions.


    (a) The difference in value at the end of year 1 is:
    . . . . . \$37,200 - 31,500\:=\:\$5,700 . . .
    Boy, that was hard!

    The percentage they asked for is: \frac{5.700}{37,200}\:=\:0.153225806\:\approx\:15.  3\%


    (b) The difference in value at the end of year 2 is:
    . . . . . \$32,550 - 26,775\:=\:\$5,775 . . .
    I need a nap!

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  5. #5
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    Quote Originally Posted by Soroban
    Hello, laser2302!

    Are you sure you can't work this out yourself?
    You know you really shouldn't be so critical, after all, people come here for reassurance and help (or, unfortunately, so they don't have to do the work) and should be treated well.
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