2. How many yards of mattin, that is half a yard wide,will cover a room that is 18 feet wide, and 30 feet long? Ans. 120 yards. 3. Suppose 800 soldiers were placed in a garrison, and their provisions were computed sufficient for 2 months; how many soldiers must depart,that the provisions may serve them 5 months? Ans. 480. 4. I borrowed 185 quarters of corn when the price was 19s. how much must I repay, to indemnify the lender, when the price is 17s. 4d. Ans. 20241. 5. A and B depart from the same place and travel the same road; but A goes 5 days before B at the rate of 20 miles per day; B follows at the rate of 25 miles per day in what time and distance will he overtake A ? Ans. B will overtake Ain 20 days, and travel 500 miles. Here two statements will be necessary; one to ascertain the time, and another to ascertain the distance. METHOD Of assessing town or parish taxes. 1. An inventory of the value of all the estates, both real and personal, and the number of polls, for which each person is rateable, must be taken in separate columns. Then to know what must be paid on the dollar, make the total value of the inventory the first term; the tax to be assessed, the second; and 1 dollar, the third, and the quotient will shew the value on the dollar. NOTE. This method is taken from Mr. PIKE's Arithmetic, with this difference, that here the money is reduced to Federal Currency. 2. MAKE a table, by multiplying the value on the dollar by 1, 2, 3, 4, 5, &c. 3. FROM the Inventory take the real and personal estates of each man, and find them separately, in the table, which will shew you each man's proportional share of the tax for real and personal estates. If any part of the tax be averaged on the polls, before stating to find the value on the dollar, deduct the sum of the average tax from the whole sum to be assessed; for which average make a separate column as well as for the real and personal estates. EXAMPLE. SUPPOSE the General Court should grant a tax of 150,000 dollars, of which a certain town is to pay Dolls. 3250,72 and of which the polls being 624 are to pay 75 cents, each ;-the town's inventory is 69568 dollars; what will it be on the dollar; and what is A's tax (as by the inventory) whose estate is as follows, viz. real 856 dollars; personal 103 dollars; and he has 4 polls? 1. As 1,75 :: 624 468 the average part of the tax to be deducted from Dolls. 3250,72 and there will remain Dolls. 2782,72 Now to find what A's rate will be. His real estate being 856 dollars I find by the Table that 800 dollars is Dolls. 32 cts. that 50 that 6 2 Ó 24 § 8 Double Hule of Chree. THE Double Rule of Three, sometimes called, COMPOUND PROPORTION, teaches, by having five numbers given to find a sixth, which, if the proportion be direct, must bear the same proportion to the fourth and fifth as the third does to the first and second. But if the proportion be inverse, the sixth number must bear the same proportion to the fourth and fifth, as the first does to the second and third. RULE. "1. STATE the question, by placing the three conditional terms in such order, that that number which is the cause of gain, loss, or action, may possess the first place; that which denotes space of time, or distance of place, the second; and that which is the gain, loss, or action, the third.” "2. PLACE the other two terms, which move the question, under those of the same name. "3. THEN, if the blank place, or term sought, fall under the third place, the proportion is direct, therefore, multiply the three last terms together, for a dividend, and 'the other two for a divisor; then the quotient will be the answer." "4. BUT if the blank fall under the first or second place, the proportion is inverse, wherefore, multiply the first, second, and last terms together, for a dividend, and the other two, for a divisor; the quotient will be the answer," EXAMPLES. 1. IF 100 dollars gain 6 dollars, in 12 months, what will 400 dollars gain in 8 months? Statement of the question. D. M. D. 100: 12::6 Terms in the supposition, or conditional terms. Or the three conditional terms, it is evident, that 100 dollars put at interest is that one, which is the cause of gain; consequently, 100 dollars must be the first term; and because, 12 months is the space of time in which the gain is made, this must be the second term; and 6 dollars which is the gain, the third term. The other two terms must then be arranged under those of the same name. Now as the blank falls under the third place, therefore, the question is in direct proportion, and the answer is found by multiplying the three last terms together for a dividend and the two first for a divisor. 2. Ir 100 dollars gain 6 dollars in 12 months, in what time will 400 dollars gain 16? |