Unknown words problems with

Many word problems lend themselves to more than one equation with more than one variable. It s easier to write two separate equations, but it takes more work to solve them for the unknowns. And, in order for there to be a solution at all, you have to have at least as many equations as variables. 

Remember those word problems you dreaded in high school Many of them are actually easier to solve by backdoor approaches. The two techniques that follow are terrific ways to solve multiple-choice word problems that you don t know how to solve with a straightforward approach. The first technique, nice numbers, is useful when there are unknowns (like x) in the text of the word problem, making the problem too abstract for you. The second technique, working backward, presents a quick way to substitute numeric answer choices back into the problem to see which one works. 

This is very similar to creating and assigning variables, as addressed earlier in the word-problem section. In addition to identifying what is known and unknown, also take time to translate operation words into actual symbols. It is best when working with a word problem to represent every part of it, phrase by phrase, in mathematical language. 

The following example shows how this can be modeled in PHREEQC. First of all, a master- ami a solution species tritium T or T1 have to be defined. Since the input of data for log k und -gamma within the key word SOLUTION SPECIES is required, but unknown, any value can be entered here as a free parameter ( dummy , e g. 0.0). This value is not used for kinetic calculations and thus, does not cause any problems. However, all results based on equilibrium calculations (e.g. the calculation of the saturation index) are nonsense for this species . The tritium values have to be entered in tritium units. However, in order not to have to define or convert them in an extra step, they are entered fictitiously with the unit umol/kgw instead of TU in PHREEQC. As no interactions of tritium with any other species are defined, the unit is eventually irrelevant. After modeling, remember that the result is displayed in mol/kgw as always in PHREEQC and has to be recalculated to the fictitious tritium unit umol/kgw. Entering mol/kgw in the input file, the solution algorithm quits due to problems with too high total ionic strengths. 

Translate word problems and the associated diagrams into material balances with properly defined symbols for the unknown variables and consistent units for steady-state processes with and without chemical reaction. 

I think most scientists would agree with me that even if you set out with certain preconceived ideas in mind, leading you to make a certain type of experiments, you often enough end up investigating a somewhat different problem. It is true that in order to get money from the Research Council or any other foundation, you have to submit a fairly detailed description of how you plan to attack the scientific problem you have outlined to them. But anyone with experience of research knows that you will in all probability have to make a number of significant changes in the project you have described. In other words, if your project represents a real piece of research, i.e. a venture into the unknown and not just a routine investigation, there is no way you could predict the outcome of it. 

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