(8) Discount, £3 2s. 6d.; Interest, £3 3s. 4d.; Error, in

favour of person receiving discount, 10d.

(3) 20 p. c.; 133 p. c. (5) 717715 nitrogen,

181700 oxygen.

(7) 55'38 gallons.

(9) N. II cwt. I qr. ;

S. I cwt. 2 qr.;

C. 2 cwt. I qr. (11) 1250 days. (13) £2.

(15) £73 115. 11ąd. (17) 160 times.

(19) 32 p. c.

(21) 64 p. c.; 86 p. c.

(23) £1 19s. 7 d.

(2) 18 p. c.

(4) 71⁄2 p. c. ; 17 p. c.
(6) 448 cubic feet.

(8) 3; 15'7; 30°7. (10) 287.

(12) 1 P. c.
(14) £3 9s. 4 d.
(16) £250 5s. 9fd.
(18) £350.

(20) £1250.

(22) 112710.

(24) £3489 16s. 3d.

Exercise 6 (p. 427).

(1) £2000; £3387.

(3) £3012 10s.

(5) £98.

(7) 3 p. c. ; £650.

(2) £4311 8s. 9d.

(4) £50; 4 Pp. c.
(6) £3000; £97 10s.
(8) £201 125.

72 139

(13) £321 10s. 102d.; £1157 11s. 073d.;

139

£857 8s. 11d.; £643 Is. 840d.

(14) Son, £1644 7s. 6d. ; wife, £548 2s. 6d. ;
daughter, £182 14s. 2d.

(15) 1122; 1734.

(16) A's, £113 16s. 11d.; B's, £59 14s. 0114d.;

(17) 1st, £136 11S. 1149d.; 2nd, £163 18s. 439d.;
3rd, £229 9s. 825d. Each person, Is. 1d.

(18) 5904, 1476, 492.

(19) A, £4285 14s. 3 d.; B, £2857 2s. 10d.;
C, £2142 175. 1§d.; D, £1714 5s. 8 d.

(20) £13 12s. 8d.; £13 7s. 3d.
(21) A, 175; B, £291; C, £233-
(22) 10d.; 9s. 41⁄2d. ; 3s. 77d.; 2s. 9åd.

(25) Men, £37 10s.; women, £37 10s.; children, £25.

(47) £31 5s. ; £41 5s.; £52 10s. ; 2s. 6d. in the pound.

(48) 6s. 8d.

(50) 3 per cent.

(49) £3 12s.

ALGEBRA.

I. CUBE ROOT.

The cube root of a simple quantity can be found by inspection.

The cube of a is a xa x a = a3; the cube of a2 is a2 × a2 × a2 = a; the cube of a3 is a9; and so on. Thus, generally, (a")3 =an. Hence the cube root of a3 is a ; the cube root of a is a2; the cube root of ao is a3; and so on. Thus, generally,

n

an

= a3. Therefore the index of the cube root is found by dividing the index of the cube quantity by 3.

Since the cube of abc is a3b3ç3, the cube root of a31⁄23å3 is abc, or the product of the cube roots of the three factors a3, b3, c3. Similarly, 3ç3 = xyz; 2/27a3b3 = 3ab;

3/64x3y9 = 4xys.

3/8x6 = 2x2;

Since the cube of a is a3, the cube root of a3 is a; that is, the cube root of a positive quantity is positive.

Again, since the cube of

a3 is

a is — a3, the cube root of a; that is, the cube root of a negative quantity is negative. This principle may be extended thus:

The square root of a2 is either plus a or minus a.

The fourth root of a1 is either plus a or minus a.

So generally, if n be even, the nth root of a" is either positive. or negative; or, "/a" =±a.

a3 is minus a

a5 is minus a. positive, and

The cube root of a3 is plus a ; the cube root of
The fifth root of a5 is plus a; the fifth root of
So generally, if n be odd, the nth root of a" is
the nth root of a" is negative; or, an = ± α.

IV.