jsasipriya wrote: ↑Thu Jul 15, 2010 3:42 am
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?
x2 - 8x - 240 = 0
x2 - 8x + 240 = 0
x2 + 8x - 240 = 0
x2 + 8x + 240 = 0
x2 - 4x - 120 = 0
Solution:
First, let’s list the factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
We see that 2, 4, and 12 are 8 less than 10, 12, and 20, respectively. Let’s try 12 and 20 first.
Let’s say there are 20 campers. So each would have gotten 60/20 = 3 cookies. However, since 8 campers didn’t want cookies, the 60 cookies would then be distributed to 12 campers and each would get 60/12 = 5 cookies. Since this is exactly two cookies more than they would have gotten if everyone had wanted cookies, we see that there must be 20 campers.
Alternate Solution:
When 60 cookies are distributed to x campers, each camper gets 60/x cookies. Since 8 campers didn’t want any cookies, there were (60/x)*8 = 480/x cookies to be redistributed. Since these cookies were distributed to x - 8 campers, each camper got extra (480/x)/(x - 8) = 480/[x(x - 8)] cookies. We are told that this is equal to 2; hence:
480/[x(x - 8)] = 2
240/[x(x - 8)] = 1
x(x - 8) = 240
x^2 - 8x - 240 = 0
(x - 20)(x + 12) = 0
x = 20 or x = -12
Since the number of campers cannot be negative, we see that x must be 20. Thus, there are 20 campers.
Answer: E
