EXERCISES.

Ex. 1. When 7 pipes of Wine cost £ 350, what is the worth

of 4 Pipes?

Ex. 2. What is the worth of 13 pints of Alcohol, when 7 pints cost £1 11 6?

Ex. 3. What is the worth of 27 pair of Shoes, at the rate of £ 5 per dozen pair?

Ex. 4. What is the worth of 7 cwt. 3 qrs. of Figs, at £ 2 15 per cwt. ?

Ex. 5. Find the value of 4 lb. 11 oz. of Isinglass, at 27 s. 6 d. per lb. ?

Ex. 6. If 52 weeks' Wages are £ 5 5, what is the amount of 17 weeks' Wages?

Ex. 7. What is due to a servant for 25 days' Wages, at 10 guineas per annum ?

Ex. 8. What is the amount of a clerk's Salary, from the 25 th of December to the 17 th of February, at 80 guineas per annum ?

Ex: 9. If the Charges upon Goods be 8 per cent., that is, £ 8 upon every £ 100 of Goods, what is the amount of the Charges upon Goods amounting to £ 467 12 6?

Ex. 10. If Interest at 5 per cent. amounts to £ 67 4 4, what will it amount to at 4 per cent.?

Ex. 11. If 12 s. 6 d. will buy 6 lb. 4 oz. of Coffee, how much will 20 s. purchase?

Ex. 12. How much Sugar can I buy with £ 100 at the rate of 66 s. 6. d. per cwt. ?

Ex. 13. The amount of the Debts upon a bankrupt's estate is £6842, and the amount of the Assets is £ 3364, at what rate will be the Dividend in the pound upon these amounts?

Ex. 14. If Interest upon a given sum at £5 per cent. be £ 4 11 6, what will it be at 4 per cent.?

Ex. 15. If £5 of Interest requires £ 100 in money, upon what capital does the Interest amount to £ 13 12 6?

Ex. 16. If Mercury performs 32 revolutions round the Sun in 2813 of our days, how many revolutions does he perform in 87 of our years, considering each year to contain exactly 365 days 6 hours?

to say we divide by 890 lb., for the divisor only shows what part is to be taken of the dividend, or how many times the quotiert would require to be repeated to make it equal to the dividend; and it is ridiculous to say we take the 890 th lb. part.

Ex. 17. If the progress of sound be uniformly 1142 feet per second of time, in what time will the report of a piece of ordnance be heard at the distance of 23 miles ?

Ex. 18. If light move with the velocity of 200,000 miles per second, in what time would an eclipse of one of Jupiter's satellites be seen on the surface of the earth, at the distance of 437 millions of miles ?

Ex. 19. In what time would a vessel, making good a direct distance of 126 miles per day, arrive from Jamaica, supposing the whole distance to be 67 degrees of 69 miles each?

Ex. 20. If a hhd. of Sugar weighing 13 cwt. 1 qr. 17 lb. cost £ 37 72, what was it rated at per cwt.?

Ex. 21. If 37 cwt. 3 qrs. 17 lb. of Goods is carried 157 miles for £ 6 13 2, how much may be carried the same distance for £ 11 4 6?

Ex. 22. If £ 2865 bear a loss of £ 1117, how much at this rate will £ 1735 have to bear?

Ex. 23. If my Income is £350 per annum, and I spend on an average 15 s. 6 d. per day, how much can I lay by in 1 year?

Ex. 24. If my Income is £ 800 per annum, and I wish to lay by 150 guineas yearly, how much shall I have left to spend per day?

INVERSE PROPORTION.

Inverse Proportion is when of four quantities, arranged as in Direct Proportion, the fourth term is the same product of the second term, that the first term is of the third, and not the third of the first.* *

If, therefore, when the given terms of a proportion are placed in the form of question, and the third, being greater than the first, requires the fourth term to be in the same degree less than the second; or when the third is less than the first, and the fourth term is required to be in the same degree greater than the second term, the calculation of the fourth term belongs to the following Rule.

RULE OF THREE INVERSE.

Rule. Reduce, if required, the first and third terms into the same denomination; then multiply the second term by the number of the first term, and divide the product by the number of the third term.

Observe. In questions of Inverse Proportion we may divide the first and third, or the second and third, terms, by any number that will exactly divide them, but not the first and second, as in Direct Proportion.

EXAMPLE.

If 8 men can do a piece of work in 12 days, how many days will 16 men require to perform the same?

This supposes that the arrangement of the first three terms is made in the form of a question; otherwise, if the quantities are arranged according to the regular form of a proportion, that is, with the similar terms in pairs, they are then said to be inversely, or rather reciprocally, proportional, when the second term is the same product of the first that the third term is of the fourth.

EXERCISES.

Ex. 1. If the provisions of a Garrison will last 2500 men for 73 days, how long will they last when the Garrison is reinforced by 750 men?

Ex. 2. If 10 yards of Muslin 4 quarters wide are sufficient for a dress, how much will be required of Muslin which measures 5 qrs. wide?

Ex. 3. If 15 yards of Calico 4 quarters wide are sufficient to form a lining, how much will be required of Calico 3 quarters wide?

Ex. 4. If a journey be performed in 7 days, travelling at the rate of 120 miles per day, how long will it require at 150 miles per day?

Ex. 5. If I lend a friend £ 200 for 12 months, how long ought he in return lend me £ 150?

Ex. 6. If I sell out £ 754 10 0 of 3 per cent. Stock at 921 per cent. net, how much 3 per cent. Stock can I procure in exchange, if the full cost of the latter is 101 per cent.?

Ex. 7. If I sell 127 oz. 17 dwts. of old silver Plate at 5 s. 6 d. per oz. how much new Plate can I purchase with the amount, at the rate of 7 s. 9 d. per oz.?

Ex. 8. How much Silver 11 oz. 2 dwts. fine,* is equal to 37 lb. 11 oz. 10 dwts. of Silver 10 oz. 15 dwts. fine?

Ex. 1. Days 56,3

2. Yds. 8

3. Yds. 20

PRODUCTS.

Ex. 5. m. 16

6. £689 5 11

7. oz. 90 14 15

4. Days 5

8. lb. 36 9 2 18

11 oz. 2 dwts. fine means, that out of the 12 oz. of metal, here called Silver, 11 oz.

2 dwts. are fine silver, the remaining 18 dwts. being copper or other alloy.

COMPOUND PROPORTION.

Compound Proportion is a combination of two or more simple proportions, occurring in the same calculation, when the product or fourth term of the first simple proportion, forms the second term of the second simple proportion; and the product of this proportion also forms the second term of the third simple proportion, and so on, with as many simple proportions as may be given.

Instead of separately working these proportions, they may be contracted by making the multiplications in succession, and dividing the product either by the divisors in succession, or by the product of the divisors, according to the following Rule.

Rule. Make the statements of the simple proportions, making that as the common term, which is similar to the product required; mark them as being direct, or inverse, and reduce the terms, if necessary, as in simple proportion.

Then, if both, or all, the proportions are direct, or both, or all, are inverse, take the product of the numbers of the first terms, and also the product of the numbers of the third terms, and use them upon the common term as in the Rule of Three Direct or Inverse.

But if one proportion is direct and the other inverse, repeat the statement of the direct, and invert the terms of the inverse proportion, and proceed as before.

Observe. Any first term, together with any third term, may be divided by whatever number will exactly divide them; and in direct proportions, any first and second terms may also be divided; then the quotients thus obtained are to be used instead of the original terms.