Why is a balanced chemical equation necessary to solve a stoichiometry problem?
I will try an analogy. Suppose you own a shop. Why is a balance sheet and statement of accounts necessary to determine whether the shop is making money?
Clearly the shop makes purchases to stock the items for sale. The shop tries to sell them for more than its purchase price. This difference is the profit margin; if this margin is consistently high, then the shop will continue to remain in business. If the profit margin is low or negative, then the shop is likely to go belly up.
Obviously, if you own a business, you have to keep a tight watch on your accounts. To see that your expenses, your wages, your purchases, your rent, is met by your income. So much for me as a business owner.
Now as chemists we know that there is no profit motive. We know that mass is conserved in a chemical reaction, so if there are 10 g of reactants, there can at most be 10 g of product. Not only can mass be balanced in a chemical reaction, but energy transfer is also accounted for stoichiometrically. So a balanced chemical equation must be on hand to represent how both matter is transformed and energy transfers. If you have further questions or objections please voice them, and I will give it another go.