Walras wrote down four sets of equations—one representing the quantity of goods demanded, one relating the prices of goods to their costs of production, one for the quantities of inputs supplied, and one showing the quantities of inputs demanded. There are four sets of variables to solve for, namely, the price of each good, the quantity of each good sold, the price of each factor of production, and the quantity of each of those factor bought by businesses. To simplify matters, Walras added one further equation to his model, requiring that all the money received must be spent, one way or the other. But there are now more equations than unknowns. From the theory of equations, one learns that a necessary but insufficient condition for the existence of a unique solution to a system of equations is that the number of equations must equal the number of variables. Walras tackled this problem by selecting an arbitrary good, G1, whose price is designated as the standard against which the prices of the other goods shall be compared. The system of equations can now be solved for the prices of all goods in terms of G1, though not for the absolute price levels.