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Plugging In: Basic Technique

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. [[snippet]] 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. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]] 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.
$$\frac{z}{4} + 5$$
$$\frac{3z+20}{4}$$
$$3z+2$$
$$3z+6$$
$$z+3$$