## Combining the two principles of algebra to solve more complicated problems

**If Ax + B = C, what is x?**

Now, we need to be able to use these two principles of algebra together to solve more complicated problems:

If we have *numberofbooks* books and also a *weightofcheese* block of cheese in our bag, and it weighs *weightofbag*, then how much does each book weigh (assuming that the books are all identical)?

So, to solve this, we could break the problem into two steps - what is the weight of all these books together *weightofallbooks* (= *numberofbooks * weightofabook*)?

We can determine this:

*weightofallbooks + weightofcheese = weightofbag*

*weightofallbooks = weightofbag - weightofcheese*

*numberofbooks * weightofabook = weightofallbooks*

*weightofabook = weightofallbooks/numberofbooks*

*weightofabook = (weightofbag - weightofcheese)/numberofbooks*

Alternately, we can do the whole thing at once. Turning our description into a statement of the weight of the bag:

*numberofbooks * weightofabook + weightofcheese = weightofbag*

*weightofabook*= something."

In this case, the required actions are exactly the same as we took above - first you subtract *weightofcheese* from both sides:

*numberofbooks * weightofabook = weightofbag - weightofcheese.*

*numberofbooks:*

*weightofabook = (weightofbag - weightofcheese)/numberofbooks*

The same result as above.

This rule works, in general, for problems of any degree of complication. However, for problems much more complictated that this one, there are no generals, simple, ways to isolate the unknown quantity.

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