This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1850 edition. Excerpt: ...of each were cut down, and then there were four times as many gooseberry-trees as apple-trees. How many were there of each at first? Let x be the number of apple-trees at first, then 3x= gooseberry-trees at first, Afterwards x-4 = number of apple-trees, and 3x--4 = gooseberry-trees, therefore, by the question, 3x-4 = 4(-4), or 3x--4 = 4x--16, transposing, 16-4 = 4%--3 x, .: 12 = x, the number of apple-trees at first, and 36 = 3x, gooseberry-trees at first. Prob. 6. The date of the accession of Geo. III. is represented by 1800-2x, that of Geo. IV. by 1800 + x2.r, that of Will. IV. by I800 + x3x; and if Geo. Ill.rd's reign be increased by 2x, it will amount to 00 years. What are the actual dates? The length of Geo. Ill.rd's reign = 1800 + x 2x-(1800-2x), = 1800 + x-1800 + 2x, = 3x.: by the question, 3t + 2x = 100, or, 5 =100, .: x =---= 20. 5.-. accession of Geo. III. is A.d. 1800-40, or 1760. Geo. IV 1800 + 20, or 1820. Will. IV 1800 + 30, or 1830. Strictly speaking Geo. III. did not reign full 60 years, having ascended the throne, Oct. 25,1760, and died Jan. 29, 1820. Prob. 7-Divide 42 into 4 parts which shall be 4 consecutive numbers. Let x be one part, then x + 1, x + 2, x + 3, are the other parts, and x + (x + 1) + (x + 2) + (x + 3) = 42, by the question, combining, 4x + 6 = 42, 4x = 36, .. x = 9; and x + 1 = 10, x + 2 11, x + 3 = 12;.--9, 10, 11, 12, are the required parts. Prob. 8. A man dies and leaves a widow, two sons, and three daughters; and in his will he orders that his personal property, amounting to l700. shall be so divided, that the three daughters shall have as much as the two sons, and the widow as much as a son and a daughter together. What are their respective shares? Let x be a son's share, then...