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 163
... pence . Now the first part was to the latter ::: . How much was sold of each ? Since ::: 9 : 8 , Let 9x = the number of lbs . of the former ; .. sx = the number of lbs . of the latter ; .. 9x = the number of shillings the first sold for ...
... pence . Now the first part was to the latter ::: . How much was sold of each ? Since ::: 9 : 8 , Let 9x = the number of lbs . of the former ; .. sx = the number of lbs . of the latter ; .. 9x = the number of shillings the first sold for ...
Page 164
... pence . 58. A Gentleman gave in charity £ 46 ; a part thereof in equal portions to 5 poor men , and the rest in equal portions to 7 poor women . Now a man and a woman had between them £ s . What was given to the men , and what to the ...
... pence . 58. A Gentleman gave in charity £ 46 ; a part thereof in equal portions to 5 poor men , and the rest in equal portions to 7 poor women . Now a man and a woman had between them £ s . What was given to the men , and what to the ...
Page 169
... pence ; after which she found that instead of making her money again , as she expected , she lost four - pence by them . How many eggs of each sort had she ? Let x = the number required ; then 2 : 2 :: 1 : the price of eggs at 2 a penny ...
... pence ; after which she found that instead of making her money again , as she expected , she lost four - pence by them . How many eggs of each sort had she ? Let x = the number required ; then 2 : 2 :: 1 : the price of eggs at 2 a penny ...
Page 171
... pence , and I buy 100 apples and pears for nine - pence halfpenny , how many of each shall I have ? Let x = the number of apples ; ..100- x producing Simple Equations . 171.
... pence , and I buy 100 apples and pears for nine - pence halfpenny , how many of each shall I have ? Let x = the number of apples ; ..100- x producing Simple Equations . 171.
Page 172
... pence a quart , and the other 12 pence ; from which he would mix a quart to be worth 14 pence . How much of each must he take ? Let x = the quantity of the first , the whole quart being represented by unity ; ..1 - x = the quantity ...
... pence a quart , and the other 12 pence ; from which he would mix a quart to be worth 14 pence . How much of each must he take ? Let x = the quantity of the first , the whole quart being represented by unity ; ..1 - x = the quantity ...
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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 quantities 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 multiplying every term number of days number of gallons number of shillings number of terms number of yards pence pieces problem proportion px² quotient 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 ах зу ху
Popular passages
Page 22 - 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.
Page 249 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards ; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space.
Page 376 - 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.
Page 369 - 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 229 - 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 155 - 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 373 - 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 363 - 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 186 - 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.