Paula has two pieces of wire, one 96 feet long and the other 72 feet long. if she wants to cut them up to produce many pieces of wire that are all of the same length, with no wire left over, what is the greatest length, in feet, that she can make them

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If you pull the information into a mathematical context, you'll notice it is asking for the highest common factor of the 2 numbers

Let's put both of them in prime factorization:

96 = 2^5 x 3

72 = 2^3 x 3^2

Now pick out what is common in these

2^3 x 3 = 24

Thus it would be 24 feet

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step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.