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Applications of Percentage.
233. Taxes. A tax is a sum of money paid for public purposes. A tax on property is reckoned at a certain per cent of the assessed value of the property. The assessed value may or may not be the real value. It is often much below the real value.
PROBLEMS. 1. Mr. Hardy has a farm of 240 acres which he values $24000. Its assessed value is $ 22 per acre. If his state tax is 1 %, his county tax 14 %, his town tax 4 %, his school tax 2%, and his special road and bridge tax 1%, how much money must he pay as taxes on his farm?
2. The assessed value of the taxable property of a certain school district is $176242.25. If the school tax is 21 % and the collector receives 2% of the amount collected as his commission, and collects the entire amount of the tax, how much should the district officers receive from this source for school purposes ?
3. The assessed value of Mr. Randall's property is $3400. At the rate of 15 mills on a dollar, * how much tax must he pay?
4. The assessed value of the property of a district of a certain city is $250000. (a) What must be the per cent of taxation to raise $10000 ? (b) What will be the net sum realized for public purposes if the collector is able to collect only 95% of this tax and he receives for his services 2% of the amount collected ?
5. Mr. Evan's tax is $35.60; the rate of taxation is 22 %. What is the assessed value of his property ? + (P. 345.)
*"15 mills on a dollar" is the same as 14%. + $35.60 is what part of the assessed value ?
7 Applications of Percentage. 234. Insurance is a guaranty by one party to pay a certain sum to another party in the event of loss or damage.
The policy is the written contract given by the underwriter to the insured. The premium is the sum paid for insurance.
PROBLEMS. 1. A store valued at $ 7500 was insured for $5000 for 1 year.
The rate of insurance was 2%. What was the amount of the premium?
2. A stock of goods valued at $10000 was insured for $5000. A fire occurred, but part of the goods were saved. It was found that the entire loss to the owner of the goods was $4750. (a) How much should he receive? (b) How much should he receive if the loss were $5750 ? *
3. An insurance agent offers to insure my farm buildings for $3500 for 1 year at 1%, or for 5 years at 3 %; the entire premium in either case to be paid in advance. (a) If I accept the first proposition, how much is the premium to be paid? (b) How much if I accept the second ?
4. What is the rate of insurance on the nearest store and stock of goods ? On farm property ? On village or city property other than stores ? †
5. A large building was insured in one company for $25000, in another company for $15000. It was damaged by fire to the extent of $12800. How much of the damage should each company pay ?
NOTE. — The companies must share the loss in proportion to the amount of insurance carried by them.
* In case of total loss the owner would receive $ 5000. In case of partial loss the owner should receive the full amount of the loss, provided it does not exceed $ 5000.
† Any insurance agent will be willing to answer these questions for you.
235. MISCELLANEOUS PROBLEMS IN APPLICATIONS OF
1. A dealer who had marked goods 50 % above the cost, sold them after deducting 10 % from the marked price. His profit on that sale was what per cent of the cost of the goods?
2. By selling a suit of clothes for $7.20 I would lose an amount equal to 10% of the cost. For what must I sell the suit to gain a sum equal to 10% of the cost ?
3. I sold goods at a loss of 7%. My actual loss was $3.50. What was the cost of the goods ?
4. The real value of a stock of goods was $8250. They were insured for $5500. A fire occurred and the salvage amounted to only $575. If the insurance company promptly settles in accordance with the above facts, what is my actual loss by the fire ?
5. If I sell goods on a commission of 121 %, what must be the amount of my sales in order that I may receive an annual salary of $2500 ?
6. A school numbers 140 pupils. The absence for one week was as follows: Monday, 3 days; Tues., 5 days; Wed., 4 days; Thurs., 5 days; Friday, 3 days. (a) What was the per cent of absence ? (b) What was the per cent of attendance ?
7. Sold a horse for $120 and gained 25%. What did the horse cost. me?
8. When the cost is of the selling price what is the gain per cent?
9. When the selling price is į of the cost what is the loss per cent?
10. The sum collected was $2321.50; com nission for collecting was 6%. What was the cost of collecting?
Algebra. 236. MISCELLANEOUS PROBLEMS. 1. In a school there are 896 pupils. There are three times as many boys as girls. How many girls? How many boys ?
2. A man had 235 sheep. In the second flock there were 15. more sheep than in the first. In the third flock there were 20 fewer than in the first. How many sheep in each Aock ?
NOTE. — Let x = the number in the first flock; then x + 15 = the aumber in the second, and x — 20, the number in the third.
3. A man owns three farms. In the second there are half as many acres as in the first. In the third there are twice as many acres as in the first. In all there are 560 acres. How many acres in each farm ?
4. In an apple and pear orchard containing 296 trees, there were 5 more than twice as many apple trees as pear trees. How many of each kind ?
5. To a number I add one half of itself and 15 and have 150. What is the number?
6. From three times a number I subtract of the number and 5, and have 37 remaining. What is the number?
Let x = the number; then 3 x – + 5 = 37. On removing the parenthesis, what sign must be changed ? 67, II.
7. If to three times a number I add s of the number and 18, the sum will be 238. What is the number?
8. Two thirds of a number is equal to the number decreased by 56. What is the number?
= x – 56
237. MISCELLANEOUS PROBLEMS.
1. A is 50 years old. B is 20 years old. In how many years will A be only twice as old as B?
NOTE. — Let x= the number of years ; then (20 + x) x 2 = 50 + x.
2. Find four consecutive numbers whose sum is 150. NOTE. - Let x = the first; then x + 1 = the second; x+ 2 = the third, etc.
3. Find three consecutive numbers whose sum is 87.
4. Two numbers have the same ratio as 2 and 3, and their sum is 360. What are the numbers ?
- Let 2 x = the first, and 3 x = the second.
5. Two numbers have the same ratio as 3 and 4, and their sum is 168. What are the numbers ?
6. Two numbers have the same ratio as 2 and 5, and their difference is 87. What are the numbers ?
7. A has $350. B has $220. How many dollars must A give to B so that each may have the same sum ?
NOTE. — Let x= the number of dollars that must be given by A to B; then 220 + x = 350
8. C. has $560. D has $340. How many dollars must C give to D so that each may have the same sum ?
9. E has $630. F has $240. How many dollars must E give to F so that E will have exactly twice as many dollars as F?
10. The fourth and the fifth of a certain number are together equal to 279. What is the number?
11. The difference between 1 fourth and 1 fifth of a certain number is 28. What is the number? (P. 346.)