# equation

• Jul 17th 2006, 09:56 PM
Judi
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
• Jul 17th 2006, 10:03 PM
malaygoel
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

Malay
• Jul 18th 2006, 07:49 AM
Soroban
Hello, Judi!

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

Quote:

Sixty cookies were to be equally distributed to $\displaystyle x$ campers.
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)

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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"?

• Jul 18th 2006, 08:31 AM
Judi
thanks...