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gether they can build it in 6 days: find the time it would take each alone.

6. Solve the equations - + - = -,- = 2, —[--==„.

'L x 1 y . z z y x z o

x _i_ 2 4 x 7

7. Solve the equation , ~ = .=.

u x — 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.

1\»

9. Expand the expression ^2 a + pj

10. What is Elimination? How many methods are you familiar with? Explain them in full

XXIII.

1. Simplify (a + b) (6 + e) (e + d) (d + a) (a + c) (b d).

2. Reduce to its simplest form ^ X 2 T" -g X

a — 6 a —

r, I .

2a; 3 /

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 f when 6 is added to its numerator, and equal to J when 2 is subtracted from its denominator?

e _ . ., ,. 2x 3 5 3x 5

6. Solve the equation ^—g = g - ^-3.

7. A and B find a purse of dollars. A takes out 2 dol

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2 X X i j. « —^— ^

6. Solve the equations y -4- ^ = g 4- 5, —j g—

_ z-4-3 _ 2y —5 _ 7 _ z_ 1Q , * — 34 12

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 f. 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 4f 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. Solve the equation ^— 1 . = r.

3. Solve the equation x* (a b -f- c) x = (6 — a)c.

ax + V. a2(b 2x)b+2b>

4. Divide 1 — by r-1! 2 b,

cr -\- ax J a -f- x

and reduce the result to its lowest terms.

5. Divide 9 a2na3n 27 a" + 27 by a" — 3.

6. Divide ft- by y/-.

7. What is the reason that aman = am+n?

XXVI.

1. Solve the equation % — 3 = 4 x -.

2. What are the three methods of Elimination? Solve the following equations by any two of the three methods: 6 x + J 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 ATs age was to N's as a' to V. Required the present ages of both.

4. Divide 1 - I X by ^"f^ - *; and

reduce the answer to its lowest terms. Simplify the division by cancelling.

5. Find the fourth term of (as b

XXVII.

1. Solve the equation — — .=—-— = -.

c ox a c

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 tfaV6 by

5. Find x from the proportion 6aTM"~2 b : x = 15a365: 40a-(ra-1,.

6. Divide a2 a ,„ by a.

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 -f- 3y -f- 2z = 40, 5x 9y 7z = 47, 9x 8y 3z = 97.

9. Find (a — &)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, 71= 16.

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4. Find (x yf and — by the Binomial

Theorem.

5. Divide 13aV — 5a413ax* + 6a* — 13a3x by 3ax + *2 — 2a?.

6. Find two numbers of which the sum is a and difference 6. 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 12asbci and 27ale'd.

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