Problems Involving an Equation

Problems involving equations can be solved in much the same way as problems involving conversions. Usually, in problems involving equations, we must find one of the variables in the equation, given the others. The conceptual plan concept outlined earlier can be used for problems involving equations. For example, suppose we are given the mass (m) and volume (V) of a sample and asked to calculate its density. The conceptual plan shows how the equation takes us from the given quantities to the find quantity. 

SORT Begin by sorting the information in the problem into given and find. 

STRATEGIZE Write a conceptual plan for the problem. Focus on the equation(s). The conceptual plan shows how the equation takes you from the given quantity (or quantities) to the find quantity. The conceptual plan may have several parts, involving other equations or required conversions. In these examples, you use the geometrical relationships given in the problem statements as well as the definition of density, d = m/V, which you learned in this chapter. 

Solve the equation(s) for the find quantity (if it is not already). Gather each of the quantities that must go into the equation in the correct units. (Convert to the correct units if necessary.) Substitute the numerical values and their units into the equation(s) and calculate the answer. 

Round the answer to the correct number of significant figures. 

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We can use a solution map for solving problems involving equations, but the solution map will take a slightly different form than for pure conversion problems. In a problem involving an equation, the solution map shows how the equation takes you from the given quantifies to the find quantity. The solution map for this problem is ... 

In this chapter, you have seen a few examples of how to solve numerical problems. In Section 2.6, we developed a procedure to solve simple unit conversion problems. We then learned how to modify that procedure to work with multistep unit conversion problems and problems involving an equation. We will now sirni-marize and generalize these procedures and apply them to two additional examples. As we did in Section 2.6, we provide the general procedure for solving nmnerical problems in the left colmnn and the application of the procedure to two examples in the center and right columns. 

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