PAPERING AND CARPETING. WALL PAPER. 230k. Wall paper is sold only by the roll, and any part of a roll is considered a whole roll. American paper is commonly yd. wide, and has 8 yd. in a roll. Foreign papers vary in width and length to the roll. Borders and friezes are sold by the yard, and vary in width from 3 in. to 18 in. Paper is also often put up in double rolls 16 yards long. It is not possible to find in advance the exact cost of papering a room, since there is frequently much waste, and a paper-hanger will charge for the number of rolls actually used in doing the work; but it is well to make an approximate estimate. EXAMPLES. 1. What would it cost to paper the walls of a room 14 ft. long, 12 ft. wide, and 8 ft. high from baseboard to ceiling, with paper 8 yd. long, and yd. wide, at $.30 a roll? OPERATION. 2 x 14 = 28 2 x 12 = 24 52 ft. 52314 yd. = SOLUTION. The distance around the room is 2 x 14 ft. + 2 x 12 ft. 52 ft. = 14 yd. 28 half yards, the number of strips required. Since the height is 8 ft., and there are 24 ft. on a roll, 1 roll will make 3 strips; and it will take as many rolls to make 28 strips as 3 is contained times in 28, which is 9+. Therefore 10 rolls will be required. At $.30 a roll, they will cost $3.00. -- RULE. I. Find the entire distance around the room in yards. Multiply this by 2 to find the number of halfyards, or strips, since the paper is only half a yard wide. II. Divide the number of half-yards by the number of strips that can be cut from a roll, and the result will be the number of rolls required. Since there are 24 ft. in a roll 8 yards long, if the distance from baseboard to ceiling is 8 ft. or less, 3 strips can be cut from a roll; if more than 8 ft. and not more than 12 ft., 2; etc. In the former case, the divisor would be 3; in the latter, 2. 2. Find the cost of papering a room 16 ft. long, 15 ft. wide, and 11 ft. high, with American paper 8 yd. long, andyd. wide, at $.50 a roll, allowing 1 ft. for baseboard, and making no deductions for openings. Ans. $10.50. 3. How many double rolls of paper 16 yd. long, yd. wide, will be required to paper the walls of a room 30 ft. long, 30 ft. wide, and 12 ft. from baseboard to ceiling? Ans. 20 rolls. CARPETS. 2301. Carpets are usually 1 yd. wide or yd. wide, and are sold by the yard. It is not often possible to find the number of yards of carpet needed by calculating the number of square yards in a floor. It is cut up into breadths which must be matched and seamed together, and more or less of the carpet is wasted in matching. A carpet with small figures usually loses less in matching than one with large figures. If neither the length nor the width of the room is a multiple of the width of the carpet, a certain amount must be turned under at the end or side, which causes another loss. EXAMPLES. 1. How many yards of carpet will be required to carpet a room 20 feet long by 13 ft. wide, with carpet yd. wide, if the strips run lengthwise? the strips run across the room? How much if SOLUTION. Since the carpet is 27 in. wide and the room 13 ft. or 162 in. wide, when laid lengthwise we will require 6 breadths of carpet of the required length. And since the room is 20 ft. or 240 in. long, it will require as many yards for each breadth as 36 in., or 1 yd., is contained times in 240 in., which is 63 yd. Hence for 6 breadths, or strips, it will require 6 x 6 yd., or 40 yd. If laid crosswise, we will need as many strips as 27 in., the width of the carpet, is contained times in 240 in., the length of the room, which is 8; therefore we will need 9 strips, and will be turned under. We will need as many yards for each strip as 36 in., or 1 Hence for 9 strips yd., is contained times in 162 in., which is 4 yd. it will require 9 times 4 yd., or 40 yd. OPERATION. 131 ft. = = RULE. Find the number of breadths or strips required, and the length of each strip. 2. How many yards of carpet, 1 yd. wide, will be required for a room 18 ft. long and 18 ft. wide, if the strips run lengthwise? If they run crosswise? Ans. 36 yd. 3. Compute the cost of carpeting a room 161 ft. long and 15 ft. wide with carpet of a yard wide, running lengthwise of the room, at $1.30 per yard. 4. Find the cost of a carpet & yd. wide, at $1.50 per yard, for a room 17 ft. long and 14 ft. wide, there being a waste of 1 yd. in matching the pattern, and the carpetlayer having been instructed to lay the carpet in the most economical way. Ans. $59.50. PERCENTAGE. 231. The term per cent is from the Latin per centum, and means by the hundred. Any per cent of a number is a certain number of each one hundred parts. By 5 per cent is meant 5 cents of every 100 cents, $5 of every $100, 5 bushels of every 100 bushels, etc. Therefore, 5 per cent equals 5 hundredths=.05=180-26; 8 per cent=8 hundredths =.08=180-25 232. Rate per cent, or rate, is the decimal which denotes how many hundredths of a number are to be. taken. The sign of per cent is %. Since per cent is any number of hundredths, it is usually expressed in the form of a decimal; but it may be expressed either as a decimal or as a common fraction. 233. Percentage is such a part of a number as is indicated by the rate per cent. Thus, 5% of 100 5. 5% is the rate per cent, and 5 is the percentage. 234. The Base of percentage is the number on which the percentage is computed. 1. The amount is the sum obtained by adding the base and percentage. It is equal to 100% + the rate per cent. 2. The difference is the remainder obtained by subtracting the percentage from the base. It is equal to 100%- the rate per cent. EXAMPLES. 1. Express, using the sign: 3 per cent; 6 per cent; 9 per cent; 14 per cent; 24 per cent; 40 per cent; 1221 per cent; 150 per cent. 2. Express, using the sign: 6 per cent; 8 per cent; 33 per cent; 7 per cent; 103 per cent; 95 per cent; 103 per cent; 225 per cent. 3. Express decimally per cent; & per cent; per cent; per cent; per cent; 1 per cent; 24 per cent; 4 per cent; 5 per cent; 7 per cent; 12 per cent; 25 per cent. 4. Express in the form of common fractions, in their lowest terms: 6 per cent; 8 per cent; 12 per cent; 141 per cent; 183 per cent; 214 per cent; 31 per cent; 371⁄2 per cent; 40 per cent; 112 per cent; 225 per cent. |