EXAMPLE V. A merchant, sending an adventure to fea, doubled his stock; by his second voyage he loft 1200l. ; by his third he doubled his remaining stock, and by his fourth lost 1 200l. ; after which he had nothing left. Required his original stock. Suppose his stock & pounds. 2d voyage, 2x=-1200 4x=3600 When there are two unknown quantities, the conditions must be such as to afford two equations; from each of these equations exterminate one of the unknown quantities; then form a new equation, by placing its values equal to one another. This new equation contains only one unknown quantity, and is resolved as before. EXAMPLE I. Two men discoursing of their money, says A to B, give me 4 shillings and I fall have three times as much as you have. B said, Give me 6 shillings of yours, and each of us will have equal shares. Required how much each had. Suppose A had x and B y shillings. Anf. x=20, and y=8. 3 H EXAMPLE EXAMPLE II. Two travellers, A and B, met at an inn. A asked B how fár he had travelled. B answered, that he had travelled so many miles and furlongs. Well, says A, I travelled only half that distance; and the number of miles I travelled corresponds with your furlongs, and my furlongs with your miles. How far did each travel ? Let x represent the miles, y the furlongs. Then A travels 8x+y 8y+* 8xty 2 8x+y=16y+2x ox=159 B travels 5 miles 2 furlongs. EXAMPLE III, Two merchants, A and B, began trade with equal stocks ; but A, by frugality and application, gained 6cl. while B, through mismanagement and bad luck, loft 8ol. At the year's end A was 8 times richer than B. Required their original stock. Anf. 100l. QUADRATIC EQUATIONS. When the square and the root of the unknown quantity are joined together, it is called an adfected quadratic equation. RULE. RULE. Transpose the quantities till the unknown quantity stand on one fide of the equation. Divide both sides by the coefficient of the square of the unknown quantity. Add the square of one half the coefficient of the simple power to both sides of the equation. Extract the square root, and transpose the half coefficient, which gives the value of the unknown quantity. EXAMPLE I. Required two numbers whose sum is 16, and product 48. x+y=16 xy=48 x=16-Y x=48 y 16m-y=48 y y2--16y=-48 Per Rule, 1-16y+64=16 ya—168+64=16 Required two numbers whose product is 108, and sum of their squares 360. 1. A man and his wife did usually drink out a barrel of beer in 12 days; and they found, by often experience, that the wife being absent, the man drank it out in 20 days. In how many days would the wife alone drink it out at her rate of drinking? Ans. 30 days. Anf. 41. 145. be B had 400 be in conjunction, in how many hours will they be in conjunction again? Anf. In ' hour. 4. Required two numbers, such that the quot of the greater divided by the lesser may be 2 less than their difference, and their product may exceed their fum by 20. Anf. 8 and a., 5. A boy is offered 10 apples for a penny, and 25 pears for 2d: He agreed to buy 100 apples and pears together for 9 d. Required the number of each. Anf. 75 apples and 25 pears. 6. Required two numbers whose fum is 108, and proportion as 5 to 4: Anf. 60 and 48, LITERAL EQUATIONS. In literal equations unknown quantities are represented by x, y, z, as before; known quantities by a, b, c, d, &c. The rules for transposing and exterminating quantities are the same as above. When the value of the unknown quantity is thus discovered, we obtain a general theorem, which will ferve for the solution of all questions under the like conditionis. EXAMPLE I. Required a theorem for determining two numbers whose fum, s, and difference, d, are given. Let x be the greater and y the less. |