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Solving for a Specified Variable Test
About Solving for a Specified Variable:

In many cases, we are given a formula that describes a very specific relationship between two or more variables. In order to manipulate these formulas, it is necessary to solve a given formula for different variables. The key is to understand how to isolate any variable in an equation.

Test Objectives:

•Demonstrate a general understanding of how formulas work

•Demonstrate the ability to extract information from a formula based on given inputs

•Demonstrate the ability to solve a formula for a given variable

Solving for a Specified Variable Test:




#1:


Instructions: Solve for z.


a) a(b + z) = cz + q


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#2:


Instructions: Solve for p, then r, then t.


a) I = prt


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#3:


Instructions: Solve for q.


a) aq - z = bq + n


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#4:


Instructions: Solve for z.


a) $$\frac{z + c}{z + a} = m + q$$


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#5:


Instructions: Solve for a.


a) $$zn + bn = \frac{ac - dg}{a}$$


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Written Solutions:




#1:


Solution:


a) $$z = \frac{q - ab}{a - c}$$


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#2:


Solution:


a) $$p = \frac{I}{rt}$$


$$r = \frac{I}{pt}$$


$$t = \frac{I}{pr}$$


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#3:


Solution:


a) $$q = \frac{z + n}{a - b}$$


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#4:


Solution:


a) $$z = \frac{ma + qa - c}{1 - m - q}$$


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#5:


Solution:


a) $$a = -\frac{dg}{zn + bn - c}$$


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