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INVERSE PROPORTION.

RULE.

Transpose the inverse extremes; that is, set that of the first place under the third, and that in the third under the first; then work as in direct proportion.

Note. See the note in direct proportion.

EXAMPLES. 1 If 7 men can reap 84 acres of wheat in 12 days; how many men can reap 100 acres in 5 days ? If 84A.

100A. 7m.

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12

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IT 84.1.2

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7 2 If 4 dollars be the hire of 8 men for three days ; hoy many days must 20 men work for 40 dolś. answer 12 days

3 °If 4 men have 24 shillings for three days work, bow many men will earn 41. 16s. in lô days P answer 3 men.

4 Suppose the interest of 333l. 6s. 8d. for 9 months be 151. what principal in 12 months will gain 6l. ?

5 If 200lb. be carried 40 miles for 40 cts.; how far may 20200lb. be carried for 60,60 ?

answer 60 miles, 6 If 145 men can make a wall 82 feet high and 40 feet long in 8 days; in how many days can 68 men build a wall 28 feet high of the same length ? answer 14 days, 11h.

uns. 1002

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PROOF. Practice may be proved by varying the parts ; by compound multiplication; or by the single rule of three direct.

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CASE 1.
When the price of an integer is less than a penny;

RULE. Take such aliquot part or parts of the given quantity, as the price is of a penny, for the answer in pence; which reduce to pounds. Note 1. When the complement of the given price, in any case, is an aliquet

part, deduct the said aliquot part of the given quantity therefrom, and the remainder will be the answer, of the same denomination with the integer of which the divisor is a part. When a remainder occurs in any example, either in this or the following cáses, let it be reduced to the next lower denomination, &c.

EXAMPLES.

VA

I 2

EXAMPL S. 1 76121b, at & per 1b. and at .. 17 6 1 2

7

6 I 2

1903 1903

12)5 70g 2101 15 18 7

210)4 715 9 facit £7 18 7

6.23 15 9

ko so do 6812 at

facit 14 3.10 3 47.12 at

14 14

6 4 15344 at á

15 19

8
5 7672 at s
6
9424 at

299

CASE 2. When the given price of an integer is a penny, or more, but less than a shilling ;

RULE. Take such part or parts of the given quantity, as the price is of a shilling, for the answer in shillings.

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EXAMPLES. 1 7612 yards, at id. per yard, and at id. 7 6 1 2

7 6 1 2

16 3 4 4
210 |
6 3 14 4

210)6 9 717 8
facit £:31 14 4

£. 348 178

2

1

1

d.

for so d.
8612 at id facit 44 17
3
1218 at 2

12-13. 9
4 7812 at 33 I 22 I

3 5 8120 at 4

135

6 8 6 8121 at 5

177 12 111 G

7 1218

do

£. so

d. 7

1218 at 61 facit 32 19 9
8 6120 at 71

197 12
9
7100 at 8

236 13 4
10 412 [ at 98

158 16 71 1002 at 10!

43 16 9
12 2345 at 11

is
13
6002 at 411

112 10 9
3001 at 9 S
15 7182 at 5 2
16

149 12

6
3591 at 10
17

6128 at 51
18 3064 at 11

140 8 8

CASE 3. When the given price of an integer is more than one shilling, and less than two;

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RULE. the given quantity stand for so many shillings, to which add the amount in shillings of said quantity at the overplus price, found by case I or 2, for the answer in shillings.

EXAMPLES.
1 486 gallons, at 12d., per gallon.

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facit £.24 16 14

d.
6100 at 131 facit 3432 6
3 1210 at 14

74 731 4 1260 at 15

78 ISO 5 712 1 at 161 482 301 6 2340 at 173 7 7890 at 18%

616 8 i

1.70 126

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