There were 100 chocolates in a box. The box was passed from person to person in one row. The first person took one chocolate. Ea
ch person down the row took one more chocolate than the person before. The box was passed until it was empty. What is the largest number of people that could have removed chocolates from the box? How do you know?
I didn't use a set equation to solve the problem, but I added 1+2+3+4... (and so on) until I got a number that was over 100. When I got to 14, the number reached 105, meaning that 13 people were able to get the number of chocolates that they desired. The fourteenth person was short 5 chocolates.
Please feel free to ask me any further questions you have! Have a wonderful day!
The answer is C. The numerator 7x+14 can be factored as 7(x+2). The denominator 2x^2+2x-6 can be factored as (x+2)(2x-3). The greatest common divisor of 7(x+2) and (x+2)(2x-3) is obviously x+2, which is contained in both of the two expressions.
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