an 1044. In addition to the details usually given in a bill, invoice shows the marks and the numbers placed upon each package shipped. In this invoice, the mark is given in the first column, and is the same on each case. The number of each case is written in the second column. Besides informing the receiver in what case a particular article is packed, it is required by the U. S. custom authorities. A certain percentage of cases in each invoice is examined, and their contents must agree in description, quantity, value, etc., with the invoice. Value in U.S. money, $366.53. Duty @ 50% = value= $183.27, nearly. English accountants employ to a great extent a method by aliquot parts A similar method may be used in reducing the above result to U. S. money. See Arithmetic, Art. 1005. The value of £50 is ascertained by taking of $486.65, or $243.325. £25 of £50. 5s. £; etc. In assessing duties, the government ignores fractions of cost less than ; over 50% is considered another dollar. a dollar in the The duty that would be collected upon the foregoing would be 50% of $367, or $183.50. Children should not, of course, be burdened with such details; their answer should be $183.27. Some zealous teachers fall into the mistake of endeavoring to make their pupils familiar with the methods of calculation peculiar to some callings. The time assigned to the study of arithmetic can be employed more profitably to the scholar by giving him the ability to handle ordinary problems with reasonable readiness, than by dissipating his energies in trying to make him understand a multitude of small matters that are entirely outside of his present experience. The average boy would make a better accountant if he did not hear of taxes, partnership, insurance, bonds, stock, brokerage, commissions, etc., during his school life, provided the time thus misspent were given to elementary algebra and constructive geometry, as well as to better work in what are considered the more elementary portions of arithmetic. 1046. The ratio of 3 to 6 is generally expressed as 1 to 2. 1049. 3. The ratio of the price of coffee to that of sugar is, or 5 to 1. 4. A goes 14 times as fast as B. The ratio of A to B is §, or = twice radius 1050. 6. One wheel makes 70 revolutions per second; the other makes 90 per second. 7. The diameter = 4 ft. goes the same distance 124.6 160 = $9201.52. Interest for 1 yr. on one-half of the cost = $230.04; $4600.76+$230.04 $4830.80, amount of mortgage. Deducting $500 then paid, gives $4330.80, balance due. = 4. Number of cubic feet of excavation 41 × 8 × 33 10890. The inner dimensions of the cellar are 38 x 30 x 8, deducting from the length and the breadth 3 ft., which is the thickness of two walls. The number of cubic feet in the cellar 9180, leaving 10890 cu. ft. — 9180 cu. ft. = 1710 cu. ft. as the contents of the walls. The cost of the excavation is $× 10890 ÷ 27 $2014; to lay the wall, costs $15 x 17.1 = $256.50. Total cost, $201.66+$256.50 = $458.16%, or $458.17. Ans. = = NOTE. One of the practices of builders in some sections is to take only the outside measure of walls in ascertaining the contents. The number of cubic feet in this case, according to their calculations, would be (41 + 33 +41 + 33) × 8 × 1 = 1782 cu. ft., or 72 cu. ft. too many. By this method the four corners, measuring each 1 × 14 × 8, or 72 cu. ft. in all, are included twice. As has already been said, children should be expected to obtain only the correct results, leaving later experience to furnish information as to local usages. = 5. For $107.25 there can be obtained, at 31%, insurance amounting to $107.25.0325 $3300. If this is 80% of the value, the flour must have cost him $3300 = $4125, which is $4125500, per barrel, or $8.25. x= the cost per barrel. = x × 500 × 80% x 31% 107.25; 500x13x=107.25; X= 8.25. = 6. The bank discount is calculated on the sum due at maturity, which is $1250+ interest from June 12 to Dec. 15 (12), 186 da. (183 da.), at 5% $1250 $32.29 ($31.77) $1282.29 ($1281.77). The discount for 30 da. (including grace) on $1282.29 at 6% is $6.41, making the proceeds $1275.88. The discount on $1281.77 for 27 da. (no grace) at 6% = $5.77, making the proceeds $1276. 8. A furnished 5 men for 20 da. and 6 men for 15 da., which is the same as 100 men and 90 men for 1 da. B furnished the equivalent of 120 men + 180 men for 1 da. The money received should be divided on the basis of 190 men for A and 300 for B, 490 in all; and A should receive 188 of the sum, and B 300 of it. 188 of $857.50 $332.50, A's share; 9. Arrange the work so as to have the required term in the last place: A ditch (403 × 3 × 3) cu. ft. is dug in (62 × 13) hr. by 27 men. A ditch (750 × 4 × 3) cu. ft. is dug in (250 × 12) hr. by ? men. If (403 × 3 × 3) cu. ft. are dug in (62 × 13) hr. by 27 men, 1 cu. ft. will be dug in (62 × 13) hr. by 1 cu. ft. will be dug in 1 hr. by 27 men 27 men x 62 x 13 NOTE. The words after deducting his commission" mislead some pupils, who think that this requires them to begin work by deducting a commission of of the amount sent. If the purchasing agent did not receive money in advance, he would render his employer the following account: To 256 bbl. flour @ $5.75, $1472.00 36.80 $1508.80 21% on the amount sent, $1508.80, would be 21% of the cost of the flour, $1472, and 21% of the $56.80 commission. A pupil that wishes to deduct the commission first, may work in this way: Let x= commission, then 40x x= cost of flour; 41x=1508.80; x = 36.80. $1508.80, amount sent, - $36.80, commission, chase of the flour. = $1472 left for the pur The commission to be deducted is of the sum sent. 1052. See Arithmetic, Arts. 936, 937. 1053. Pupils generally find it most convenient to change the time to days, leaving the reduction to lowest terms for the subsequent cancellation. 11. 2 yr. 11 mo. 18 da. = 720 da. + 330 da. +18 da. = 1,068 yr. 712x=3204; x= = 4. The teacher will notice that canceling 100 and 356 by dividing each by 4, and reducing the equation to 178x = = 32.04, is of no advantage. The French method of solving an example like the foregoing, is to indicate all the work, and then to cancel : The The first member of equation (a) is "cleared of fractions" by multiplying the second number by the compound denominator, 100 × 360; see (b). value of x is then found by dividing the second member by the compound coefficient of x, 240 × 1068; see (c). The result is then obtained by cancellation. In practice, the second equation (b) is not employed, the multiplication by 100 × 360, and the division by 240 × 1068, being indicated at the same time. |