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13 extracting 15 whence A's gain A's stock addition Clearing the equation Clearing the second completing the square distance equation by 12 equation multiplied equation of fractions extracting the root extracting the square gallons of brandy hence latter least common multiple length Let 3x Let x zz lO0x Multiplying both sides Multiplying every term Multiplying the numerator Multiplying the second Multiplying this equation number B travels number killed number of bushels number of days number of gallons number of hours number of miles number of shillings number of women number of yards number remaining numbers are 12 numerator and denominator quantity pumped second equation Silenus square root squaring both sides subtraction sum saved Transposing and completing transposition weight whence 2x whence x whence x2 жу Зж Зу уг Уж Шу
Page 142 - ... pieces of land, which are in the form of rectangular parallelograms. The longer sides of the two are in the proportion of 6 to 11, and the adjacent sides of the less are in the proportion of 3 to 2. The whole distance round the less is 135 yards greater than the longer side of the larger piece. Required the sides of the less, and the longer side of the greater. 27. A person distributes forty shillings amongst fifty people, giving some 9d. and the rest 15d. each. How many were there of each ?...
Page 153 - Let 5x zz the number of apples, .'. 5x — 180 = the number of oranges, and 5 : 3 : : 5x : the price of the apples, — 3x, In the same way, the price of 35 apples = 21d.
Page 228 - On the 31st day, the quantity drunk was 172 ; on the 32d, 169 ; and thus the quantity of water consumed daily, after 30 days, forms a decreasing arithmetical progression, whose common difference is 3, and number of terms x — 9.
Page 217 - B's throw out as much as 5 of A's, the water thrown out in a given time by A is to that thrown out by B : : 6 : 5.
Page 151 - Let 5x — the rate required, 6 : 4 : : 18 : the distance he can row with the tide, per hour, = 12, .'. 12 — 5x = the distance without the tide, and...
Page 161 - Let x =: the number of gallons of strong beer, and as £12| = the duty on the ale, and £50 what he sells the ale for...
Page 230 - Let x - the number of merchants, and у =: the number of months at the end of which the captain was entitled to a £100 share ; 25 .'. у : 25 : : 1 : — =. the number of the captain's shares, У 25ж = the middle term, and у •= the common ratio, .-. — + 25.
Page 211 - / =: the time in which Bacchus would empty the cask, and 3x = the time in which Silenus would empty it, .'. 2x = the time Bacchus drank, 2x and y : 1 : : 2x : the quantity Bacchus drank = — , У 2x .'. 1 -- =: the quantity Silenus drank ; У 2x 6я?