CHAPTER XVIII.
Problems leading to Simultaneous Equations.
178. In the Examples discussed in the last chapter we have seen that it is essential to have as many equations as there are unknown quantities to determine. Consequently in the solution of problems which give rise to simultaneous equations, it will always be necessary that the statement of the question should contain as many independent conditions as there are quantities to be determined.
Ex. 1. Find two numbers whose difference is 11, and one-fifth of whose sum is 9.
Let X represent the greater number, y the less.
Then x-y=11 (1).
Also, {x+y}{6} = 9, or x + y = 45 (2).
By addition, 2 x = 56 ; and by subtraction, 2 y = 34.
The numbers are therefore 28 and 17.
Ex. 2. If 15 lbs. of tea and 10 lbs. of coffee together cost $15.50, and 25 lbs. of tea and 13 lbs. of coffee together cost $24.55, find the price of each per pound.
Suppose a pound of tea to cost x cents and a pound of coffee to cost y cents.
Then from the question, we have 15 x + 10y = 1550 (1), 25 x + 13 y = 2455 (2).
Multiplying (1) by 5 and (2) by 3, we have 75 x + 50 y = 7750, 75 x + 39 y = 7365.
Subtracting, 11 y = 385, y = 35.
