Ax. 1. If equals be multiplied by equals, the products will be equal.

Ax. 2. If equals be divided by equals, the quotients will be equal.

2. If 15 bushels of oats cost $4.50, what will 75 bushels cost?

15 bu. = $4.50. Divide both members by 15.

1 bu. =

.30. Multiply both members by 75. 75 bu. = $22.50.

3. If 20 bushels of wheat yield 4 barrels of flour, how many bushels will yield 15 barrels of flour ?

4 barrels = 20 bushels.
1 barrel = 5 bushels.

15 barrels = 75 bushels. 4. A man bequeathed his estate of $10000 to his son and daughter; the son to have $2000 more than the daughter. What was the share of each ?

The work may be shortened by letting x represent one of the unknowns; thus, Let

= daughter's share.

X + 2000 = son's share. Add the 2 shares, 2x + 2000 = 10000

8000

4000 daughter's share.

X + 2000 I 6000 son's share. COR. 1. If equals be subtracted from equals, the remainders will be equal.

2. If equals be divided by equals, the quotients will be equal..

5. A and B hired a pasture for $55; A paid 13 dollars more than B. What did each pay?

2x =

EQUATION OF PAYMENTS consists in averaging the time of several payments so as to get the time when all may be paid at once, without loss to either party; thus,

1. Bought goods for $300 payable in 2 months, $500 in 3 months, $700 in 4 months. At what time should the whole be paid without loss to either party? = 3145

$300 x 2 $600 in 1 month.
500 x 3 1500 in 1 month.

1700 X 4 = 2800 in 1 month.

$1500 x 34 = $4900 in 1 month. The discount of 4900 for 1 month = 1500 in 31. months. The whole should be paid in 3 mo. 8 da., Ans.

2. Bought goods for $500 payable in 30 days, $600 in 60 days, $1000 in 90 days, $5000 in 120 days. What would be the equated time to pay the whole?

30

15000 60

36000 90

90000
5000 x 120

600000
7100 x 10441 = 71 ) 741000 ( 1044 days.

71
310
284

22

500 x 600 x 1000 x

AVERAGING ACCOUNTS.

When sales are made at different times and on different teams, to find on mean time when all may be paid without loss to either party; thus, 1. A merchant sells goods as follows:

Jan. 1st, $100 on 1 month.
Jan. 18th, 200 on 1 month.
Feb. 1st, 300 on 2 months.
Feb. 12th, 250 on 3 months .

At this date no payment has been made. In how many days should the whole be paid at once in order to secure both parties? Begin at Feb. 1st, when the first account is due.

Feb. 1st, $100 x 0
Feb. 18th, 200 x 17 = 3400
Apr. 1st, 300 x

1st, 300 x 59 = 17700
May 12th, 250 x 100 = 25000
850

) 46100 ( 54 days.
4250

3600
3400

2010

= to

850 Due 54 days after Feb. 1st; that is, 27th March.

2. When an account has both debits and credits, begin with the first date.

DR. B. THOMPSON in acccount with I. PARSONS. CR
To invoice of goods due

March 15th, $400 March 1st, by cash, $300
April 1st, 300 April 1st, by cash, 200
April 15th, 200 April 15th, by cash, 300
May 1st, 400 May 15th, by cash, 500

May 15th, 600
Before conjoined.
$400 X 14 = $5600

300 x 0 300 x 31 = 9300

200 x 31 = $6200 200 x 45 = 9000

300 x 45 = 13500 400 x 61 = 24400

500 x 75 = 37500 600 x 75 = 45000

$1300

$57200 $1900

$93300 1300

57200 $600 6 ) 361|00

60 days.

a

a

CONJOINED EQUATIONS AND RATIOS consist of a number of equations, and in each successive equation the left hand member or antecedent is a like term of the right hand member or consequent of the preceding equation.

PROBLEMS. 1. If 5 oranges are worth 8 lemons, 3 lemons worth 10 apples, 4 apples worth 1 melon, and 6 melons worth 75 cents, how much are 12 oranges worth? Arrange in equations.

1 apple

6 x 4
10 apples = 75 x H x 40 = 3 lemons.
8 lemons = 75 x H x L x = 5 oranges.

25

2

4

12 oranges = 7$ x x x x = 25 x 2 x4=200 $La

x

2. If 6 cords of wood buy 12 barrels of apples, 8 barrels of apples buy 6 barrels of oranges, 2 barrels of oranges 32 lbs. butter, 40 lbs. butter = 1 ton coal, and 6 tons coal = 15 barrels flour, how many cords wood will 12 barrels flour buy? wood. apples. 6 = 12 oranges. 8 = 6 butter. 2 = 32

coal.
40 -1 flour.
6 – 15

12 = how many cd. wood: 1 bbl. apples = Poz 8 bbls. apples = 6x = 6 bbls. oranges. 2 bbls. oranges = 6x = 32 lbs. butter.

12 x

. 40 lbs. butter

= 6 x x x = 1 ton coal. 6 tons coal = 6 x 19 x8 xf = 15 bbls. flour.

. .

2 1

2

12 bbls. flour

= 2x2x2 = 8 cords of wood. CoR. 1.—When the odd term, which is the term of demand, is the consequent of the last equation, make it