X 2 gether they can build it in 6 days: find the time it would take each alone. 2 1 3 3 2 1 1 4 6. Solve the equations - + 2, + 3 y Y 4 7. Solve the equation 1 2 x 3 8. The length of a rectangular field exceeds the breadth by one yard, and the area is three acres; find the dimensions. x + 2 = ~ اجت 9. Expand the expression (2a + )?. 62 10. What is Elimination? How many methods are you familiar with ? Explain them in full. XXIII. 1. Simplify (a + b)(b + c) — (c + d) (d + a) – c (a + c)(b — d). at x2 2. Reduce to its simplest form a + b Х X a 72 a2 + x2 x 4. Find a number such that three times its square diminished by five times the number itself shall amount to 50. Solve completely. 5. What fraction is that which becomes equal to when 6 is added to its numerator, and equal to 1 when 2 is subtracted from its denominator? 3 5 - 5 6. Solve the equation 5 2 3 7. A and B find a purse of dollars. A takes out 2 dol lars and of what remains; B takes out 3 dollars and I of what then remains. They find that each has taken out the same amount. How many dollars were there in the purse? = 8. Solve the equations 73 — 3y= a, 53 - 11y = a, 9y — 5%= a. XXIV. 1. Find the value of a + 2 x — {b+y -[a — * — -[a (6 — 2 y)]} when a = 2,6 = 3,x= 6, and y= 5. ] , 5 2. Divide 1 - 6 a® + 27 a4 by } + 2a + 3 az. 6 a* 3. Reduce to its lowest terms 205 a” 2030 90 90 27 4. Find both roots of the equation 3 + 1 X x + 2 = 0. 5. Expand, by the Binomial Theorem, (m n)5 and 21 (va — 3 = +5,*71 3 4 7. A man hires a certain number of acres of land for $ 336. He cultivates 7 acres for himself, and lets the rest for $4 an acre more than he pays for it. He receives for the portion that he lets what he pays for the whole, or $ 336. Find the number of acres. 8. The value of a fraction, if its numerator is doubled and its denominator increased by 7, is f; while, if its denominator is doubled and its numerator increased by 2, its value is . What is the fraction ? XXV. C 1. A certain piece of work can be done by A and B working together in 3f days, by B and C in 44 days, and by C and A in 6 days. Required the time in which either can do it alone, and the time in which all can do it together. 2 + 20 9 2. Solve the equation 2 5 3. Solve the equation 22 (a − b + c) x= (b − a) c. b C. a? — (6 — 2 x) 6 + 262 4. Divide 1 by 26, a+ a a a + and reduce the result to its lowest terms. 5. Divide 9 a 2n 27 a" + 27 by a" - 3. X a x + 62 Qin 6. Divide Vi by Van 7. What is the reason that am a" = am+n? XXVI. 15 1. Solve the equation x - 3= 4x — 2. What are the three methods of Elimination ? Solve the following equations by any two of the three methods : 6 x + y = 0,2 (4x — 1)=3(y - 8). 8 3. M's age is to N’s as a is to b; but c years ago M's age was to N's as a' to 6. Required the present ages of both. ' 208 and (2 — 3) (x + 2) reduce the answer to its lowest terms. Simplify the division by cancelling. vol 5 2 4. Divide 1 – x2 + by XC ; X 3 5. Find the fourth term of (a26 — ) ax с a XXVII. 6 1. Solve the equation bx 2. What are eggs a dozen when two more in a shilling's worth lowers the price one penny per dozen ? 3. A merchant adds yearly to his capital one third of it, but takes from it at the end of each year $5,000 for his expenses. At the end of the third year, after deducting the last $5,000, he finds himself in possession of twice the sum he had at first. How much was his original capital ? 4. Divide $12.76 by Yab.c 5. Find x from thc proportion 6am-2b : x=15a375 : 40a-m-1). at ab 6. Divide a? by a2 62 7. What is the rule for transposing a term from one side of an equation to the other; and what is the reason of the rule ? 8. Solve the equations 4.c + 3y + 2z = 40, 5x — 9y 4x + 72 47, 92 By 32 97. 9. Find (a - b) by the Binomial Theorem. a. a XXVIII. 1. A certain sum of money at simple interest will amount to a dollars in m months, and to b dollars in n months. Find the principal and the rate of interest. Find the answers when a = 1837.50, b = 1890.00, m = n = 16. 90 2. Solve the equation 10, 27 90 = by 7 3a 4. Find (- y)5 and OC 336 and ( the Binomial 2a Theorem. 5. Divide 13a%a2 5a4 13ax + 624 - 13aRx by Зах + а2 202 6. Find two numbers of which the sum is a and difference b. State a rule for finding two numbers when their sum and difference are given. 7. Find the greatest common divisor and the least common multiple of 12a%bc4 and 27abcd. |