LESSONS IN ALGEBRA. 



10. A man agreed to give a labourer 12s. a day for every day he 

 worked, but for every day ho was idle he should forfeit 8s. 



y nettled, and their account WM oven. How 

 many days did ho work P 



1 1 . Tin. portions, A, B, and C, draw prizes in a lottery. A 



i> draws as much as A, together with a third of 

 <lr.i\vs ; and C draws as much as A and fi both. V 

 the aiiicniiit i>f tlir tliroe prizes? 



1_. What number in that whioh is to 12 increased by three 

 ho number, as 2 to 9 ? 



V ship and a boat are descending a river at the same 

 time. Tho .ship passes a certain fort when the boat is 13 miles 

 below. Tho ship descend* 5 miles, while the boat descends 3. 

 At what distance below the fort will they be together F 



1 t. What number is that, a sixth part of whioh exceeds an 

 eighth part of it by 20 ? 



15. Divide a prize of .2,000 into two such parts that one of 

 thorn shall be to tho other as 9 to 7. 



li>. What sum of money is that whose third part, fourth 

 part, and fifth part, added together, amount to .94 ? 



17. Two travellers, A and B, 360 miles apart, travel towards 

 each other till they meet. A's progress is 10 miles an hour, and 

 B's 8. How far does each travel before they meet ? 



18. A man spent one-third of his life in England, one-fourth 

 of it in Scotland, and the remainder of it, which was 20 years, 

 in the United States. To what age did he live ? 



iy. What number is that, | of which is greater than of 

 it by 96 ? 



20. A post is J, in the earth, f in tho water, and 13 feet above 

 the water. What is the length of the post ? 



21. What number is that, to which 10 being added, f of the 

 sum will be 66 ? 



22. Of the trees in an orchard, J are apple-trees, fa pear- 

 trees, and the remainder peach-trees, which are 20 more than 

 J of the whole. What is the whole number of. trees in the 

 orchard ? 



23. A gentleman bought several gallons of wine for J694 ; 

 and after using 7 gallons himself, sold * of the remainder for 

 .20. How many gallons had he at first P 



24. A and B have the same income. A contracts an annual 

 debt amounting to f of it ; B lives upon ^ of it ; at the end of 

 ten years B lends to A enough to pay off his debts, and has 

 .160 to spare. What is the income of each ? 



25. A gentleman lived single i of his whole life ; and after 

 having been married 5 years more than } of his life, he had a 

 son, who died 4 years before him, and who reached only half tho 

 age of his father. To what age did the father live ? 



26. What number is that, of which if , , and '-, bo added 

 together, the sum will be 73 ? 



27. A person after spending .100 more than \ of his income, 

 had remaining .35 more than \ of it. Required his income. 



28. In the composition of a quantity of gunpowder, the nitre 

 was lOlbs. more than of the whole, the sulphur 441ba. less 

 than i of the whole, the cliarcoal 21bs. less than of the whole. 

 What was the amount of gunpowder ? 



29. A cask which held 146 gallons, was filled with a mixture 

 of brandy, wine, and water. There were 15 gallons of wine more 

 than of brandy, and as much water as the brandy and wine to- 

 gether. What quantity was there of each ? 



30. Four persons purchased a farm in company for ^4,755 ; 

 of which B paid three times as much as A ; C paid as much as 

 A and B ; and D paid as much as C and B. What did each 

 pay? 



31. It is required to divide the number 99 into five such parts 

 that the first may exceed the second by 3, be less than the 

 third by 10, greater than the fourth by 9, and less than the fifth 

 by 16. 



32. A father divided a small sum among four sons ; the third 

 had 9 shillings more than the fourth, the second had 12 shillings 

 more than tho third, the 5rst had 18 shillings more than the 

 second, and the whole sum was 6 shillings more than 7 times 

 the sum which the youngest received. What was the sum 

 divided ? 



33. A farmer had two flocks of sheep, each containing the 

 ame number. Having sold from one of these 39, and from tho 

 other 93, he finds twice as many remaining in the former as in 

 the latter. How many did each flock originally contain ? 



34. An express travelling at the rate of 60 miles a day, had 



been dispatched 5 days, when a second WM sent after him, 

 travelling 75 mile* * day. In what time will tho one overtake 

 the other ? 



85. A'H age is doable that of B, and B's age triple tint of C, 

 and tho Hum of all their age* 140. What is the age of each ? 



86. Two piece* of cloth, at the name price by the yard, bat of 

 different length*, were bought, the one for b, and the other for 

 .6*. If 10 yard* be added to the length of each, the MUM will 

 be a* 5 to 6. Required the length of each piece. 



37. A and B began trade with equal Bam* of money. The 

 first year A gained .40, and B loct 440. The eeoond year A 

 loot i of what ho had at the end of the first, and B gained 440 

 less than twice the sum whioh A had lo*t B bad then twice 

 as much money as A. What sum did each begin with f 



38. What number U that, whioh being severally added to 36 

 and 52, will make the former Hum to the latter M 3 to 



39. A gentleman bought a chaise, bone, and harness for 4360. 

 The horse cost twice as much a* the harness, mad the chaise 

 cost twice as much as the harness and hone together. What 

 was the price of each ? 



40. Out of a cask of wine, from whioh had leaked J part, 21 

 gallons were afterwards drawn ; when the cask was found to be 

 half full. How much did it hold ? 



41. A man has 6 sons, each of whom is four yean older tb*n 

 his next younger brother ; and the eldest is three times as old 

 as the youngest. What is the age of each P 



42. Divide the number 49 into two such parts, that the 

 greater increased by 6, shall be to the less diminished by 11 M 

 9 to 2. 



43. What two numbers are as 2 to 3 ; to each of which, if 4 

 be added, the sums will be as 5 to 7 P 



44. A person bought two casks of porter, one of which held 

 just three times as much as the other ; from each of these Ike 

 drew 4 gallons, and then found that there were 4 times as many 

 gallons remaining in the larger as in the other. How many 

 gallons were there in each ? 



