Combining the two principles of algebra to solve more complicated problemsIf 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 Then, we simply need to take the required actions so that we are left with "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.
- 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.