Jacoby is using a bucket to collect nuts from a nut tree. He then dumps the bucket into a barrel for shipping of the nuts. He notices that 1 over 5 bucket of nuts fills 2 over 3 of the barrel. Write and solve an equation to find the number of buckets that will fill the entire barrel. Be sure to define your variable and show your work. Explain your answer in words. (10 points)

You need 3/10 buckets of nuts to fill the barrel.

Step-by-step explanation:

We know that 1/5 of a bucket of nuts, fills 2/3 of the barrel.

Then how much we need to fill the other 1/3 of the barrel?

1/3 = (2/3)/2

Then we need half of 1/5 buckets of nuts, this is:

(1/5)/2 = 1/10 buckets of nuts.

Then we need in total:

1/5 + 1/10 buckets of nuts.

we can multiply and divide the left fraction by 2, to get:

(2/2)*(1/5) + 1/10 = 2/10 + 1/10 = 3/10

You need 3/10 buckets of nuts to fill the barrel.

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