Intellectual Algebra, Or Oral Exercises in Algebra, for Common Schools ...
Burgess, 1853 - 208 pages
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added to three added to twice Anna Anna's apples balls weigh barrel bought Charles complete the square condition cost cube root difference Dividing each member dollars Eliza's equa equal number equation will express equation will represent express the product express the quotient express the remainder express the sum expression will represent fraction gave George George's gives greater be added greater number half horse Intellectual Algebra John last term less number Let x represent miles money multiplied Multiplying each member nine ninths number be added number is four number of books oranges peaches pears perfect square pupils question Reduce the equation represent the number represent the remainder represent the sum respective values root of x² second root seven sevenths sheep six pounds sixth smaller number square root taken from twice three fifths three fourths twelve twenty twenty-four twice the greater twice the less Uniting terms value of x
Page 191 - The sum of two numbers is 32, and if the greater be divided by the less, the quotient will be less than 5 but greater than 2.
Page 37 - Therefore, by the conditions of the qiAstion, 6z = 24; and, dividing each member by 6, x =^- ; that is, x is £ of 24, which is 4. Then he bought 4 apples, 4 lemons, and 4 oranges. » 15. The sum of three numbers is sixty-three. The first is twice the second, and the second is twice the third. What are the numbers ? 16. A horse, saddle, and bridle, together, cost one hundred and forty-four dollars. The saddle cost twice as much as the bridle, and the horse three times as much as the saddle and bridle...
Page 190 - The sum of two numbers is 6, and the sum of their 5th powers is 1056. What are the numbers?
Page 66 - There are ninety sheep in a flock, owned by three men. A owns twelve more than B, and C owns fourteen less than A and B both. How many sheep does each own 1 13. The sum of three numbers is seventy. The first is eleven more than the third, and the second is as much as the first and third together, lacking twelve. What are the numbers? 14. Three men together have
Page 119 - The sum of two numbers is a, and their difference is b; what are the numbers? Let x — the greater number, and
Page 163 - In the expression z2 -f- 6 x, what term is wanting to make the expression a perfect square ? Extracting the square root of z2, the first term of the expression, gives x for the first term of the root. Since 6 z is twice the product of the two terms of the root, if 6...
Page 109 - What did one of each coat? 15. There are two numbers, such that, if three times the greater be added to three times the less, the sum will be twenty-one ; and if three times the less be taken from five times the greater, the remainder will be nineteen. What are the numbers ? 16. If -three times Anna's age be added to three times Mary's age, the sum will be thirty-three years ; and three times Mary's age is thirty-seven years less than seven times Anna's. What are their respective ages ? and four...
Page 191 - The sum of the squares of two numbers is 170, and the difference of their squares is 72. What are the numbers ? 4.
Page 99 - A and B gain money in trade, but A receives ten dollars less than B. If A's share be subtracted from twice B's, the remainder will be fifty-seven dollars. How much money did each receive ? 28.
Page 118 - SECTION XXIV. 1. A BOY bought five oranges and two lemons for twenty-six cents, and a lemon cost one cent less than an orange. What was the price of one of each ? Let x — the price of an orange, and y ~ the price of a lemon. (1.) By a condition of the question, . . . .x — y=l. (2.) By another condition, 5x-|-2y = 26. (3.) Multiplying 1st by 2, 2* — 2y = 2. §24.] (5.) Dividing 4th by 7, . . x = 4, price of an orange. (6.) Subtracting 5 x from each ) „ — o« _ c member of 2d, .... i ' (7.)...