Suzy is using a bucket to collect nuts from a nut tree. She then dumps the bucket into a barrel for shipping of the nuts. She notices that 1 over 2 the bucket of nuts fills 2 over 3 of the barrel. Part A: Write and solve an equation to find the amount of nuts that will fill the entire barrel. Show your work. (8 points)

Part B: Explain your answer in words. (2 points)

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  a) b = (1/2)/(2/3); b = 3/4

  b) it takes 3/4 bucket to fill a barrel

Step-by-step explanation:

a) Apparently, the number of buckets and the number of barrels is proportional, so we can write an equation for b, the number of buckets to fill a barrel, as ...

  buckets/barrels = b/1 = (1/2)/(2/3) . . . . the equation

Of course, b/1 = b, so we simply need to simplify the compound fraction to find the solution.

  b = (3/6)/(4/6)

  b = 3/4 . . . . the solution to the equation

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b) The solution to the equation is the answer to the question. It takes 3/4 bucket of nuts to fill the barrel.

the least common denominator is 40