A flock of $$z$$ birds lands on a fig tree. One-fourth of the birds fly away while 5 more birds land on the same tree. In terms of $$z$$, how many birds are now on the tree?

Correct.
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When $$z=4$$, this answer choice yields
>$$\displaystyle \frac{3z+20}{4} = \frac{3(4)+20}{ 4} = \frac{32}{ 4} = \color{blue}{8}$$,
so it matches your *goal*. All other answer choices are eliminated by this Plug-In, so this is the right answer choice.
>A) $$\frac{z}{4} + 5 = \frac{4}{4} + 5 =\color{red}{6}$$, which is not equal to your goal of 8. __POE__.
>C) $$3z+2 = 3(4)+2 = \color{red}{14}$$, which does not equal to 8. __POE__.
>D) $$3z+6$$. This choice is even greater than C. __POE__.
>E) $$z+3 = 4+3=\color{red}{7}$$, which is not equal to 8. __POE__.

Incorrect.
Notice that $$\frac{1}{4}$$ of the birds fly *away*, while the question asks for how many birds *remain* on the tree.
This is exactly the type of careless mistakes that __Plugging In__ helps you avoid. __Plugging In__ good numbers forces you to work out the problem step by step instead of jumping to conclusions based on what you *think* you've read.

Incorrect.
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Incorrect.
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Incorrect.
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Did you try to __Plug In__ $$z=8$$ and get more than one answer choice? In that case, __POE__, then change numbers and __Plug In__ again for the remaining answers only.

$$\frac{z}{4} + 5$$

$$\frac{3z+20}{4}$$

$$3z+2$$

$$3z+6$$

$$z+3$$