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• Explanation.—The three hogs came to $41,95; therefore, $41.95 divided by the whole weight, will give the average price per pound. . - Ans. 4}}} cents.
2. If 50 gallons of brandy, worth 6 shillings per gallon : 45 gallons worth $1.05 per gallon, be mixed with 33 gallons, worth 96 cents per gassion, what will be the value of one gallon of the mixture ? .
- Aus. 100,’’, cents.
3. A and B agreed to settle a disputable account on the average judgment of three men, who all declared a balance in favour of B. C's judgment was $14, D's $15,96, E's $12,34. Agreeably to the decision. what aught A to pay B Ans. $14,10.
4. P wishing to build a brick house, agreed with R to furnish brick for $233,334. The house was 40 feet long, 35 feet wide, and the walls were 18 feet high and 1 foot thick. There were 30 windows, each 5 ft. 6 in. high, and 2 ft. 10 in. wide. Making no allowance for doors, what did R receive per thousand for his brick.
Brick are generally made 8 inches long, 4 inches wide, and 2 inches thick. Ans. $4.
5. If three clerks can copy 180 pages in two days, how many pages can 7 clerks copy in 6 days, working at the same rate 2
First find how many pages one will copy in one day, then how many pages he will copy in 6 days. - Ans. 1260.
6. If 200 dollars in 14 months gain 14 dollars interest, how much interest will 300 dollars gain in 13 months, at the same rate 2 Ans. $19,50. 7. If 6 men can perform a piece of work in 58 days, in how many days can 10 men do # of the same work, working at the same rate 2 Ans. 27#4. 8. If $594 will pay the board of 11 men 9 weeks, how many men can be boarded 12 weeks, at the same rate per week, for $1080 ° Ans. 15.
9. A man bought 300 pairs of shoes for $225, and exchanged 180 pairs for 150 hats. He then gave 100 hats for 90 yards of cloth, and sold the cloth for $108. What did he gain per cent. ” Ans. 20.
10. A gentleman bought 95 yards of cloth, ; of a yard wide, for 100 dollars, and gave the same and $25 for cloth of the same quality, one yard wide. How many yards did he buy 7 Ans. 891';.
11. The distance of West Point from the city of New-York, is 60 miles. A performed a journey on foot from the latter to the former place in 12 hours. After travelling 4 hours, he inquired the remaining distance, and was answered, that the distance he had already travelled, equalled # of the remaining distance. How far had he travelled, and at what rate did he travel per mile before and after making the inquiry.
Explanation.—If the distance he had travelled be divided into parts equal to those into which the remaining distance is supposed divided, that is, so that each part should equal # the remaining distance, there would be 3 parts, for the distance travelled is equal to # the remaining distance, and those 3 parts added to the 7 parts remaining, gives 10, the number of parts into which the whole is divided. A had travelled over 3 of these parts, consequently he had travelled for of the whole distance.
Ans. He had travelled 18 miles. His average speed before the inquiry was 44 miles per hour, and after 5}.
JNote—Answers to all questions similar to the last, may be found by making the sum of the given numerator and denominator, the denominator, and preserving the given numerator.
12. A certain philosopher being asked at what time he arose in the morning, answered, that the time he usually spent in bed after midnight, was equal to # of the time intervening between the time of his rising and twelve o’clock at noon. Required the time. -- Ans. At half past 4 o'clock.
13. A certain clerk receives for his services $800 a year. His expenses equal or of what he saves. How much of his salary does he save yearly 2 - Ans. $550. 14. R and S received the same income yearly. R spent 3 of his, S spent $40 more than R, which involved him in debt $10 a year. What was their yearly income 2
Explanation.—Had S spent but $30 more than R, he would have just spent his income, for $40 is $10 more than one-fourth of R's income. Ans. $120.
For working questions similar to the last, see rule page 175. -
15. F and H traded upon equal capitals, F gained a sum equal to # of his capital,—and H a sum equal to ; ; of his which was $500 less than F's gain. What was the capital of each 3 Ans. $4000.
16. A can earn 6 shillings a day. A and B can earn twice as much as C; but A and C can earn 3 times as much as B. What can B and C earn respectively 2
Explanation.—The labour of C equals , the labour of the three, and the labour of B equals of the labour of the three, both of which will perform so of the whole ; therefore 6 shillings divided by or, the part that A can perform, will express what the three can earne Ans. B can earn 33 s. and C, 43 s.
17. Divide 144 into two such parts, that when the less is multiplied by 9 and the greater by 7, their products may be equal. Ans. 63 and 81. 18. A merchant paid $2934 for a quantity of rum, brandy and whisky,_giving 8 shillings a gallon for brandy, 6 for rum, and 3 for whisky. The brandy equalled # the quantity of rum, and the rum + the quantity of whisky. How many gallons of each kind did he purchase ? * Ans. Brandy 40 gal; rum, 120, and whisky, 240. 19. A gave $350 for two pieces of cloth,-one measuring 24 yards, and the other 31. The price per yard of the smaller, was to that of the larger piece as 5 to 74. What did he give per yard for each piece? Ans. $4+; ; for the less, and $734 for the other.
A tax is money assessed on the polls and properties of individuals for the purpose of supporting government, schools, highways, &c.
In general, the tax on each poll is fixed at a certain rate, which is first taken out of the whole tax, and the remaining part of the tax is assessed upon the property of the town, parish, district, &c. An inventory is taken of all the taxable property, both real and personal of the whole town, parish, or district; also of each individual who is to be taxed. Then each individual is taxed in proportion to his property. After knowing the amount of the inventory and the whole tax, the most convenient method of finding the tax of each individual, is to write in a table the tax upon any number of cents from 1 to 10; for 20, 30, 40, &c. to 100 cents; also the tax upon any number of dollars from 1 to 20, or a greater number if necessary. By knowing the property of any individual, it will be easy to ascertain his proportion of the tax by adding together those sums standing against his amount of property in the table. If the tax on each poll be a fixed sum, that sum should be multiplied by the whole number of polls, and the product subtracted from the whole tax as in the following example.
Suppose a tax of $5138,20 be assessed upon a town, the inventory of which is $25691 ; and that there are 209 polls, which pay 25 cents each. What will be the tax on one dollar of the inventory !
The tax on the 209 polls is $52,25, which taken from the whole tax $5138,20, leaves $5085,95 to be assessed upon the property. The remaining part of the tac must be divided into as many equal parts as there are dollars in the inventory, to ascertain what must be paid upon one dollar of the inventory. This we shall do by dividing 508595 cents by 25691, the number of dollars contained in the inventory.
Ans. The tax on one dollar will be 19,7+-cents.
If the tax on each poll be established at a certain rate, the amount of the polls is considered a part of the inventory, and will pay a tax equal to the same amount of the inventory of the property, consequently their amount must be added to the inventory of the property.
Suppose the inventory of the property in a certain town, to be $41265; the number of polls 360; and that each poll is rated by law at $1,20. If a tax of $83.39.40 be assessed on this town, what will be G’s tax, who pays for 2 polls, and whose property is valued at $46,27 ?
Explanation.—360 the number of polls, multiplied by $1,20, must be added to the inventory of the property. . Then $8339,40 divided by $4.1697, gives 20 cents the tax on one dollar; and 20 cents divided by 1 dollar, gives two mills the tax on one cent.
To form a table, we multiply 2 mills by 2, 3, 4, &c. cents, and 20 cents, by 2, 3, &c. dollars.