4. A can do a piece of work in 6 days, and B in 5 days. How long will it take both together to do it? cent. 5. Find the interest of $2750 for 3 years at 4 per 6. Find the interest of $950 for 2 years 6 months at 5 per cent. 7. Find the amount of $2000 for 7 years 4 months at 6 per cent. 8. Find the rate if the interest on $680 for 7 months is $35.70. 9. Find the rate if the amount of $750 for 4 years is $900. 10. Find the rate if a sum of money doubles in 16 years 8 months. 11. Find the time required for the interest on $2130 to be $436.65 at 6 per cent. 12. Find the time required for the interest at 5 per cent on a sum of money to be equal to the principal. 13. Find the principal that will produce $161.25 interest in 3 years 9 months at 8 per cent. 14. Find the principal that will amount to $1500 in 3 years 4 months at 6 per cent. 15. How much money is required to yield $2000 interest annually if the money is invested at 5 per cent? 16. Find the time in which $640 will amount to $1000 at 6 per cent. 17. Find the principal that will produce $100 per month, at 6 per cent. 18. Find the rate if the interest on $700 for 10 months is $25. CHAPTER XI. SIMULTANEOUS SIMPLE EQUATIONS. 184. If we have two unknown numbers and but one relation between then, we can find an unlimited number of pairs of values for which the given relation will hold true. Thus, if x and y are unknown, and we have given only the one relation x + y = 10, we can assume any value for x, and then from the relation + y = 10 find the corresponding value of y. For from x+y= 10 we find y = 10- If x stands for 1, y stands for 9; if x stands for 2, y stands for ; if x stands for 2, y stands for 12; and so on without end. x. 185. We may, however, have two equations that express different relations between the two unknowns. Such equations are called independent equations. Thus, x+y= 10 and x- -y= =2 are independent equations, for they evidently express different relations between x and y. 186. Independent equations involving the same unknowns are called simultaneous equations. If we have two unknowns, and have given two independent equations involving them, there is but one pair of values which will hold true for both equations. Thus, if in § 184, besides the relation x + y = 10, we have also the relation x - y = 2, the only pair of values for which both equations will hold true is the pair x = 6, y = 4. Observe that in this problem x stands for the same number in both equations; so also does y. 187. Simultaneous equations are solved by combining the equations so as to obtain a single equation with one unknown number; this process is called elimination. There are three methods of elimination in general use: I. By Addition or Subtraction. 189. To Eliminate by Addition or Subtraction, therefore, Multiply the equations by such numbers as will make the coefficients of one of the unknown numbers equal in the resulting equations. Add the resulting equations, or subtract one from the other, according as these equal coefficients have unlike or like signs. NOTE. It is generally best to select the letter to be eliminated that requires the smallest multipliers to make its coefficients equal; and the smallest multiplier for each equation is found by dividing the L. C. M. of the coefficients of this letter by the given coefficient in that equation. Thus, in example 2, the L. C. M. of 6 and 8 (the coefficients of x) is 24, and hence the smallest multipliers of the two equations are 4 and 3, respectively. Sometimes the solution is simplified by first adding the given equations or by subtracting one from the other. |