## 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 Equations of Higher Dimensions |

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Page 198

... of barley . 20. A number consisting of 2

... of barley . 20. A number consisting of 2

**digits**when divided by 4 , gives a certain quotient and a remainder of 3 ; when divided by 9 gives another quotient and a remainder of 8. 198 Examples of the Solution of Problems. Page 199

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**digit**on the left hand is equal the quotient which was got when the number was divided by 9 ; and the other**digit**is equal , th of the quotient got when the num- ber was divided by 4. Required the number . Let x and y the**digits**in ... Page 245

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**digits**, the quotient is two , and if 27 be added to it , the**digits**will be inverted ? Let x and y be the**digits**; .. 10x + y = the number , 10x + y and = 2 ; xy .. 10x + y = 2xy ; also 10x + y + 27 = 10y + x ; by transposition , 9x + ... Page 268

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**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 x X - y represent the**digits**; then ... Page 269

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**digits**are 2 , 3 , and 4 , and the number = 234 . = 3. The sum of £ 1 . 78 , 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 ...### Other editions - View all

### Common terms and phrases

3x²y addition answer the conditions arithmetic series arithmetical progression casks common difference completing the square containing cost cube digits distance Divide the number equal equation ³ equation of fractions equation x² extracting the root extracting the square find the values former gain geometric series geometrical progression Given 3x Given x Given x² greater guineas harmonic progression least common multiple length less Let 4x number of days number of gallons number of pounds number of shillings number of terms number of yards pence pieces problem proportion px² Quadratics received Required the number second equation sheep shil sold square root squaring both sides Substituting this value subtraction third three numbers Transform the equation transposition travelled unknown quantity values of x wheat whence whole number x²y x²y² xy² зу ху

### Popular passages

Page 24 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.

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Page 378 - From two places at a distance of 320 miles, two persons, A and B, set out at the same time to meet each other. A travelled 8 miles a day more than B, and the number of days in which they met was equal to half the number of miles B went in a day. How many miles did each travel, and how far per day ? 20.

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Page 371 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...

Page 231 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately 1 Ans.

Page 157 - His head weighed as much as his tail and half his body, and his body weighed as much as his head and tail together. What was the weight of the fish ? Let 2x = the weight of the body in pounds.

Page 375 - A gentleman bought two pieces of silk, which, together, measured 36 yards. Each of them cost as many shillings per yard as there were yards in the piece, and their whole prices were as 4 to 1. What were the lengths of the pieces ? Solution.

Page 365 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in...

Page 188 - Prob. 3. Find two numbers, the greater of which shall be to the less, as their sum to 42 ; and as their difference to 6.