gether they can build it in 6 days: find the time it would take each alone. 8. The length of a rectangular field exceeds the breadth by one yard, and the area is three acres; find the dimensions. 9. Expand the expression (2 a + 1). 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) — a2 10 3 3. Find the first four terms of (27 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 6 is added to its numerator, and equal to tracted from its denominator? when when 2 is sub 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 of what then remains. They find that each has taken out the same amount. How many dollars were there in the purse ? 9y 8. Solve the equations 7x-3y=a, 5x-11ya, 1. Find the value of a + 2x {b + y — [a — x — y = 5. 6 a2 + 27 a2 by + 2a+3a2. 5. Expand, by the Binomial Theorem, (m y 6. Solve the equations y + = + 5 = 1 - 5 3 2 12' 4 - 2 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 ; while, if its denominator is doubled and its numerator increased by 2, its value is . What is the fraction? XXV. 1. A certain piece of work can be done by A and B working together in 3 days, by B and C in 42 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. What are the three methods of Elimination? Solve the following equations by any two of the three methods: 6x+y=0,2 (4 x — 1) = 3 (y 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 b'. Required the present ages of both. хв x; and reduce the answer to its lowest terms. Simplify the divis ion by cancelling. 5. Find the fourth term of (a2 6 — VG)". 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? Va5.c 4. Divide a√b by 5. Find x from the proportion 6am-2b: x=15a365 : 40a-(m-1). 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 4x+3y+2z — 40, 5x — 9y— 7% = 47, 9x 8y 3z 9. Find (ab)7 by the Binomial Theorem. 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 = 10, n = 16. 2. Solve the equation 1837.50, |