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Thread: Find Percent For Last Year

  1. #1
    Super Member harpazo's Avatar
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    Find Percent For Last Year

    Last year Ginger saved 10 percent of her annual earnings. This year she earned 5 percent more than last year and saved 12 percent of her annual earnings. The amount saved this year was what percent of the amount saved last year?

    Last Year: 0.10x

    This Year: 0.05 + 0.12x

    I concluded the equation to be:

    (0.05 + 0.12x) = 0.10x

    This led to -2.5 as a value for x.

    Book's answer is 126 percent.
    What is the correct equation set up?
    Can someone explain this problem sentence by sentence leading to the correct equation?
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    Re: Find Percent For Last Year

    Quote Originally Posted by harpazo View Post
    Last year Ginger saved 10 percent of her annual earnings. This year she earned 5 percent more than last year and saved 12 percent of her annual earnings. The amount saved this year was what percent of the amount saved last year?

    Last Year: 0.10x
    (What is x? You must always define any variable you introduce into the problem. Here x is last year's earnings. Also makes it easier for someone else to follow your steps.)

    This Year: 0.05 + 0.12x

    (When you are adding terms, always check that the terms are in the same "units". Here 0.05 represents 5%, while 0.12x represents 12% of last year's earnings (in $). %+$ doesn't make sense. 0.05x + 0.12x might be a possibility, 0.05 + 0.12 might be a possibility, but neither relate to this problem.)

    I concluded the equation to be:

    (0.05 + 0.12x) = 0.10x

    This led to -2.5 as a value for x.

    Book's answer is 126 percent.
    What is the correct equation set up?
    Can someone explain this problem sentence by sentence leading to the correct equation?

    Let x be last year's earnings.

    Last year's savings = 0.10x.


    This year's earnings = 1.05x (she earns 5% more this year)

    This year's savings = 0.12 * 1.05 x = 0.126x

    The amount saved this year was what percent of the amount saved last year?

    Can you finish it off?
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    Re: Find Percent For Last Year

    Quote Originally Posted by harpazo View Post
    Last year Ginger saved 10 percent of her annual earnings. This year she earned 5 percent more than last year and saved 12 percent of her annual earnings. The amount saved this year was what percent of the amount saved last year?

    Last Year: 0.10x
    You don't say what "x" represents but since she "saved 10 percent of her annual earnings last year I presume "x" is her last year's earnings.

    This Year: 0.05 + 0.12x
    No. "5% more than last year" is "last year" + 5% of "last year"= x+ 0.5= 1.05x. Then you take 12% that new amount: 0.12(1.05x).

    I concluded the equation to be:

    (0.05 + 0.12x) = 0.10x
    Again, no. Even if the left side were correct, this just says that the amount saved "this year" is equal to the amount saved "last year". You were not told that. Further "x" here is the amount she earned last year. You were not asked that!

    This led to -2.5 as a value for x.

    Book's answer is 126 percent.
    What is the correct equation set up?
    Can someone explain this problem sentence by sentence leading to the correct equation?
    The problem asked "The amount saved this year was what percent of the amount saved last year?"

    The amount saved this year was 0.12(1.05x)= 0.126x. The amount saved last year was 0.1x. The amount saved this year was $\displaystyle \frac{0.126x}{0.1x}$. That is $\displaystyle \frac{0.126}{0.1}= 1.26$ or 126%.
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  4. #4
    Super Member harpazo's Avatar
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    Re: Find Percent For Last Year

    Quote Originally Posted by HallsofIvy View Post
    You don't say what "x" represents but since she "saved 10 percent of her annual earnings last year I presume "x" is her last year's earnings.


    No. "5% more than last year" is "last year" + 5% of "last year"= x+ 0.5= 1.05x. Then you take 12% that new amount: 0.12(1.05x).


    Again, no. Even if the left side were correct, this just says that the amount saved "this year" is equal to the amount saved "last year". You were not told that. Further "x" here is the amount she earned last year. You were not asked that!


    The problem asked "The amount saved this year was what percent of the amount saved last year?"

    The amount saved this year was 0.12(1.05x)= 0.126x. The amount saved last year was 0.1x. The amount saved this year was $\displaystyle \frac{0.126x}{0.1x}$. That is $\displaystyle \frac{0.126}{0.1}= 1.26$ or 126%.
    Great break down of the problem.
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  5. #5
    Super Member harpazo's Avatar
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    Re: Find Percent For Last Year

    Quote Originally Posted by Debsta View Post
    Let x be last year's earnings.

    Last year's savings = 0.10x.


    This year's earnings = 1.05x (she earns 5% more this year)

    This year's savings = 0.12 * 1.05 x = 0.126x

    The amount saved this year was what percent of the amount saved last year?

    Can you finish it off?
    How did you get 1.05x?
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    Re: Find Percent For Last Year

    Quote Originally Posted by harpazo View Post
    How did you get 1.05x?
    x is last year's earnings.

    This year she earns 5% more than x.

    That's 100% of x + 5% of x = 105% of x = 1.05x
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  7. #7
    Super Member harpazo's Avatar
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    Re: Find Percent For Last Year

    Quote Originally Posted by Debsta View Post
    x is last year's earnings.

    This year she earns 5% more than x.

    That's 100% of x + 5% of x = 105% of x = 1.05x
    This is the skill I YEARN to learn. What you did is truly amazing! Wish I could do likewise.
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    Re: Find Percent For Last Year

    I had a typo in my response that I didn't find until it was too late to edit.

    I wrote ""5% more than last year" is "last year" + 5% of "last year"= x+ 0.5= 1.05x."

    Of course that last equation should have been "x+ 0.5x= 1.05x".
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    Re: Find Percent For Last Year

    NO excuses: to the corner for .5x minutes...x=60...
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  10. #10
    Super Member harpazo's Avatar
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    Re: Find Percent For Last Year

    Quote Originally Posted by HallsofIvy View Post
    I had a typo in my response that I didn't find until it was too late to edit.

    I wrote ""5% more than last year" is "last year" + 5% of "last year"= x+ 0.5= 1.05x."

    Of course that last equation should have been "x+ 0.5x= 1.05x".
    Thank you very much.
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