Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

10. If the carriage of 8 cwt. 128 miles cost $ 12.80, what must be paid for the carriage of 4 cwt. 32 miles ? Ans. $1.60. 11. If 16 L. 18s. be the wages of 16 men for 8 days, what sum will 32 men earn in 24 days? Ans. 101L. 8s. 12. If 350 L. in half a year gain 10 L. 10s. interest, what will be the interest of 400 L. for 4 years? Ans. 96 L.

INVERSE PROPORTION.

RULE.

Transpose the inverse extremes; that is, set that which is in the first place under the third, and that which is in the third place under the first; then work as in Direct Proportion.

EXAMPLES.

1. If 7 men reap 84 acres of wheat in 12 days, how many men can reap 100 acres in 5 days? Ans. 20 men.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small]

2. If 4 dollars be the hire of 8 men for 3 days, how many days niust 20 men work for 40 dollars?

Ans. 12.

3. If 4 men have $ 3.20 for 3 days work, how many men will earn $12.30 in 16 days? Ans. 3 men.

4. If 4 reapers have 12 dollars for 3 days work, how many will earn 48 dollars in 16 days?

Ans. 3.

5. If 100 L. in 12 months gain 6 L. interest, what sum will gain 3 L. 7s. 6d. in 9 months? Ans. 75 L.

6. If a footman travel 240 miles in 12 days, when the days are 12 hours long; how many days will he require to travel 720 miles when the days are 16 hours long? Ans. 27 days.

7. If 100 L. in 12 months gain 8 L. interest, what sum will gain 8 L. 12s. in 5 months?

Ans. 258 L.

8. If 200 lb. be ́carried 40 miles for 40 cents, how far may 20200 lb. be carried for $60.60?

PROMISCUOUS EXAMPLES.

Ans. 60 miles.

1. If 4 men in 5 days eat 7 lb. of bread, how much will suffice 16 men 15 days? Ans. 84 lb. 2. If 100 dols. gain Ø 3.50 interest in 1 year, what sum will gain $38.50 in 1 year and 3 months? Ans. 880 dols.

3. If it take 5 men to make 150 pair of shoes in 20 days, how many men can make 1350 pair in 60 days? Ans. 15. 4. If the wages of 6 men for 21 weeks be 120 L. what will be the wages of 14 men for 46 weeks?

Ans. 613L. 6s. 8d. 5. If 333 L. 6s. 8d. gain 15 L. interest in 9 months, what sum will gain 6 L. in 12 months? Ans. 100 L.

"

PRACTICE.

Practice is a short method of ascertaining the value of any number of articles, or of pounds, yards, &c. by the given price of one article, one pound, or one yard, &c. Practice may be proved by Compound Multiplication; or, by the Single Rule of Three Direct.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small]

An aliquot part of a number, is any number that will divide it without a remainder; thus, 4 is an aliquot part of 20, and 8 of 56. A sum or quantity is an aliquot part of a greater sum or quantity, when a certain number thereof will make the greater; thus a shilling is an aliquot part of a pound, because 20 shillings make one pound.

When the price is less than a penny, work by

RULE 1.*

If the price be a farthing, or a halfpenny, divide the given number by as many thereof as make a penny, for the answer in pence.

If the price be three farthings, find the value of the given number at a halfpenny, and afterwards at a farthing; then add the two results together, and their amount will be the answer.

When remainders occur, proceed with them as under rule 3, Compound Division.

EXAMPLES.

1. What is the value of 4528 quills, at 2. What is the value of 4528 quills, at

[blocks in formation]

each?
each?

2264 value at

1132 value at

12)3396 Ans.in pence.

[blocks in formation]

* The reason of this rule may be given thus: The value of any number of articles at a farthing, or a halfpenny, &c.each, is that number of farthings, or halfpence, &c. and to find their value in pence, shillings, or pounds, we reduce the farthings, or halfpence, &c. to pence, shillings, or pounds: thus the value of 4528 quills, at a farthing each, is 4528 farthings; which, reduced, make 4 L. 14s. 4d.— See example 1. When the price is three farthings each, the operation is somewhat different; for, this being no aliquot part of a penny, we cannot divide the given number by as many thereof as make a penny, to produce pence; we are therefore obliged to use the component parts of the price; as in example 2.

The explanation of this rule, with a little variation, will apply to each of the other rules in Practice.

[blocks in formation]

When the price is not less than a penny, but less than a shilling, and is an aliquot part of a shilling, work by

RULE 2.

Divide the given number by as many of the price as make a shilling, for the answer in shillings.

EXAMPLES.

1. What is the value of 7612 lb. of rosin, at id. per Ib. and also at 1d. per lb. ? Id. 7612 at ld.

210)63|4 4

| 14d. | | | 7612 at låd.

210)951 6

[blocks in formation]

23 15 9

14, 14 ro

95 12 3 135 6 8

69 2

U

When the price is not less than a penny, but less than a shilling, and is no aliquot part of a shilling, work by

RULE 3.

Separate the price into parts, one of which shall be an aliquot part of a shilling, and the others, either aliquot parts of this part, or of a shilling, or of one another: find the value of the given number at one or more of such parts of the price as are aliquot parts of a shilling by Rule 2; then, from the value at these parts, find the value at the rest of the price, and add the several sums together for the answer.

EXAMPLES.

1. What is the value of 6192 yards of tape, at 24d. per yard?

2. What is the value of 3711 lb. of sugar, at 72d. per lb,?

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

Answer reduced 119 L. 16s. 81d.

Note. In working the former of these examples, we find the value of the given number at 2d. by Rule 2, and divide the result by 8 to find the value at ; for as is an eighth part of 2d. the value at must be an eighth part of the value at 2d.

similar manner.

d.

3. 3596 at 21.

The latter example is wrought in a

[blocks in formation]
[blocks in formation]

123 19 2

149 12 H

109 14 6
117. 1 10

156 11 4.

313 13 2

341 1 6

140 8 8

12. 3064 at 11.

When the price is not less than a shilling, but less than two shillings, work by

RULE 4.

Let the given number stand for its value in shillings, at a shilling; find the value in shillings, at the rest of the price, and add the several sums together for the answer.

« ΠροηγούμενηΣυνέχεια »