Algebraical Problems: Producing Simple and Quadratic Equations, with Their Solutions, Designed as an Introduction to the Higher Branches of Analytics: To Which Is Added, an Appendix, Containing a Collection of Problems on the Nature and Solution of Equat
Algebraical Problems: Producing Simple and Quadratic Equations, with Their Solutions, Designed as an Introduction to the Higher Branches of Analytics: To Which Is Added, an Appendix, Containing a Collection of Problems on the Nature and Solution of Equat
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1841 edition. Excerpt: ...prices of which (in shillings) were in arithmetical progression. The price of the next above the cheapest was 8 shillings, and the price of the dearest 23 shillings. What was the price of each book? Let x--the price of the cheapest, and y = the common difference; then x + y = the price of the second = 8, and x ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1841 edition. Excerpt: ...prices of which (in shillings) were in arithmetical progression. The price of the next above the cheapest was 8 shillings, and the price of the dearest 23 shillings. What was the price of each book? Let x--the price of the cheapest, and y = the common difference; then x + y = the price of the second = 8, and x + 6y = the price of the dearest = 23;.. by subtraction, 5y = 15, and y = 3;.. x--8--y = 8--3 = 5, and /. the prices are 5, 8, 11, 14, 17, 20, 23 shillings, respectively. 2. A number consists of 3 digits, which are in arithmetical progression; and this number divided by the sum of its digits is equal to 26; but if 198 be added to it, the digits will be inverted. Required the number. Let a?--yl x represent the digits; 3. The sum of 1. 7s, was to be raised by subscription by three persons A, B, and C; the sums to be subscribed by them respectively forming an arithmetical progression. But C dying before the money was paid, the whole fell to A and B; and C's share was raised between them in the proportion of 3: 1, when it appeared that the whole sum subscribed by A was to the whole sum subscribed by B:: 4:5. Required the original subscriptions of A, B, and C. Let x--y, x, x + y, be the respective subscriptions of A, B, and C; then 3x = 27; and.. x = 9. Now 5:2:: (C"s share =) 9 + y; the part paid by B = l-(o + y), 3 and 5: 3: 9 + y: the part paid by A =-. (9 + y) be the numbers; 4. Four numbers are in arithmetical progression. The sum of their squares is equal to 276, and the sum of the numbers themselves is equal to 32. What are the numbers? Let 2y = the common difference, and x + 3y" x + y x--y x--3yi then their sum = 4x = 32, and x = 8; also the sum of their squares = 4x' + 2oy = 276, in which substituting the value of x...
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