...+ y) + b(x — y) = 1. a(x — y) + b(x + y) = 1. (34.) Divide the number 90 into four parts, such that the first increased by 2, the second diminished...third multiplied by 2, and the fourth divided by 2, may all be equal. (35.) If a2 + 62 = l = e2 + d\ show that (ad - bc) (ad + bc) = (a — c)(a + c) yS...

...2y — z = 20; 3x + 2y — z = 32. 9. Divide the number 90 into 4 parts, such that if the first be increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, the four quantities thus obtained shall be equal to each other. 10. Find the sum of the series (1)...

...¿2+cî+2ac+4aô+4ic. 601 Ci S . Solve x — о x — a 7i Divide the number 90 into four parts so that the first part increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, may be all equal. 8. What powers of a quantity are the same whether the 45. l , l 1. Simplify 1 Jl...

...$x — 3^—28 = « (5) Zx~ 2У~ 13=( 9. Divide the number 90 into 4 parts, so that the first part increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2 may be all equal. 10. A greyhound starts for a course at a distance of fifty of his own strides from...

...dollar. How many pieces of each kind must A give him ? Ans. — — ~ of the first kind ; — — ^ of the second. a— b a—b Prob. 45. Divide the number...usually introduced, but this practice is worse than superE fluous. The four parts into which 45 is to be divided may be represented thus: The first -x—2,...

...equals the number of horses. Ans. Sheep, 56 ; cows, 40 ; horses, 32. 23. Divide the number 90 into 4 such parts that the first increased by 2, the second...third multiplied by 2, and the fourth divided by 2, may all be equal. Ans. 18; 22; 10; 40. 24. A general drawing up his army in the form of a solid square,...

...equals the number of horses. Ans. Sheep, 56 ; cows, 40 ; horses, 32. 23. Divide the number 90 into 4 such parts that the first increased by 2, the second...third multiplied by 2, and the fourth divided by 2, may all be equal. Am. 18 ; 22 ; 10 ; 40. 24. A general drawing up his army in the form of a solid square,...

...would it be filled by the other alone ? Ans. 30 minutes. 57. Divide the number 90 into four parts so that the first increased by 2, the second diminished...third multiplied by 2, and the fourth divided by 2, may all be equal. Ans. 18, 22, 10, 40. 58. Divide the number 88 into four parts so that the first increased...

...cistern ? 7. Divide $90 into 4 such parts, that the first increased by 2, the second diminished bjt 2, the third multiplied by .2, and the fourth divided by 2, shall all be equal. 8. The sum of the distances 'which A, B, and 0 have traveled is 62 miles ; A's distance is. equal 'to...

...by one man. How many men were there in the regiment ? 15. Divide the number 90 into four parts such that the first increased by 2, the second diminished...third multiplied by 2, and the fourth divided by 2 will all be equal. 16. A can do half as much work as В, В can do half as much as C, and together...