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
1

9 2. Solve the equation

2
1 + 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.

'
2
1

208
1 Х

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.