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  1. #1
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    equation

    Sixty cookies were to be equally distributed to x campers. When 8 campers did not want the cookies, the other campers each received 2 more cookies. Which of the following equations could be used to find the number of campers x?
    a. X^2-8X-240=0
    b. X^2-8X+240=0
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by Judi
    Sixty cookies were to be equally distributed to x campers. When 8 campers did not want the cookies, the other campers each received 2 more cookies. Which of the following equations could be used to find the number of campers x?
    a. X^2-8X-240=0
    b. X^2-8X+240=0
    Your first equation is correct

    Malay
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  3. #3
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    Hello, Judi!

    I had to baby-talk my way through this one . . .


    Sixty cookies were to be equally distributed to $\displaystyle x$ campers.
    When 8 campers did not want the cookies, the other campers each received 2 more cookies.
    Which of the following equations could be used to find the number of campers $\displaystyle x$ ?

    $\displaystyle (a)\;\;x^2 - 8x - 240\:=\:0\qquad(b)\;\;x^2 - 8x + 240\:=\:0$

    With $\displaystyle x$ campers, each got $\displaystyle \frac{60}{x}$ cookies each.

    With $\displaystyle (x - 8)$ campers, each got $\displaystyle \left(\frac{60}{x} + 2\right)$ cookies each.


    Since the number of cookies was 60: .$\displaystyle (x - 8)\left(\frac{60}{x} + 2\right)\;= \;60$

    Multiply: .$\displaystyle 60 + 2x - \frac{480}{x} - 16 \;= \;60$

    Simplify: .$\displaystyle 2x - 16 - \frac{480}{x}\;=\;0$

    Multiply by $\displaystyle x:\;\;2x^2 - 16x - 480 \;= \;0$


    Divide by $\displaystyle 2:\;\;x^2 - 8x - 240 \;= \;0$ . . . answer choice (a)

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    I just noticed . . .

    The discriminant for equation (b) is: $\displaystyle (-8)^2 - 4(240)$ . . . negative!
    . . So equation (b) has no real roots.

    So the answer is $\displaystyle (a)$ . . . "by elimination"?

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  4. #4
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    thanks...
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