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29. An automobile passed 5 mile-posts in 8 minutes 10 seconds. How many miles per hour was it moving ?
30. It is estimated that 24 men working 18 days can repair a certain street. The contract calls for the work to be completed in 8 days. How many extra men must be employed?
31. It is estimated that 60 men can dig a sewer on Main Street in 24 days. The contract time is 40 days. How many men may be discharged and yet have the work completed within the contract time ?
32. A's property is assessed at $2750, on which $37.90 taxes are paid each year. How much tax should B pay on his property assessed at $4375 ?
33. A train of 30 cars of ore contains 1200 tons. How many cars must be added so that the train may carry 2700 tons ?
34. A city's assessed valuation is $5675000. There must be raised in taxes on this valuation $ 85125. How much is Mr. Templeton's tax on a property assessed at $15750 ?
PARTITIVE PROPORTION AND PARTNERSHIP
Partitive proportion is the process of separating a number into parts proportional to two or more numbers.
Written Work 1. Separate 180 into parts proportional to 1, 2, and 3.
Since the parts are in the ratio of 1, 2, and 3, then 1+2+3, or 6 parts = 180.
The 1st number = 180 · 6, or 30
The 3d number = 3 x 30, or 90
2. A man and two boys earn $162 and agree to divide it as follows: 3 parts to the man, 2 parts to the first boy, and 1 part to the second boy. How much should each receive ?
3. The receipts of a street railway in one month are $15600, and the expenses are to the profits as 1 to 2. Find the expenses and the net savings.
4. Four men own a gold mine valued at $805000. The parts owned by each are in the ratio of 6, 1, s, and ". Find each man's share of the mine.
5. The cost of shipping a train load of 2000 tons of iron ore from Duluth, Minn., to Bessemer, Pa., is $2800. If the lake freight is to the railroad freight as 50 to 90, find each one's share of the freight charges.
6. Two railroads, valued at $6900000 and $23000000, share charges of $ 299000 for freight carried over both roads in proportion to the valuation of each road. Find the earnings apportioned to each road.
Partnership is the associating of two or more persons who agree to combine their money, labor, goods, skill, or “good will ” in some enterprise, and to share the profits or losses of the business in proportion to the interest each partner owns.
The partnership is frequently called a firm, or a house, and derives its name from the persons that compose it; as “Brown & Hamilton.”
The capital of a partnership is the sum of the investments of the partners. This capital may be money or anything that has a money value, as skill, good will, experience, labor, etc.
Gains and losses in a common partnership are usually apportioned in proportion to the amount of capital each partner invests and the length of time such capital is invested ; but in case any partner cannot pay his proportionate share of the loss, the remaining partners are liable for the whole loss.
1. A and B engage in business; A furnishes $800 and B, $1200; they gain $500. What is each man's share ?
$800+ $1200 = $2000, entire capital
= }, A's share of the capital
= }, B’s share of the capital
$2000 : $1200 = $500 : $300 The ratio of the whole capital to each partner's investment is equal to the ratio of whole gain or loss to each partner's share of the gain or loss.
2. A, B, and C engaged in manufacturing iron. A invested $42000, B $96000, and C his skill, valued at $72000. Their profits the first year were $12600. How much was each man's gain?
3. M, N, and R formed a partnership; M furnished of the capital, N , and R the remainder. They gained $7560. What was each man's share of the gain?
4. E, F, and G engaged in merchandizing with a capital stock of $ 28000. E furnished $7000, F $ 6000, and G the remainder. They gained 142% on the investment. What was each man's share of the gain?
5. The assets of a firm that failed in business were $3750; their liabilities $ 22000. How much will two creditors, to whom they owe $7800 and $5100 respectively, receive?
6. A storeroom belonging to Smith, Jones, & Brown was entirely destroyed by fire. They received $9675 insurance. What was each man's share, if Smith owned 1, Jones, and Brown the remainder of the stock?
A's gain - 34000
7. A and B formed a partnership January 1, and each invested $2500; May 1 A added $500, and B withdrew $500. At the end of a year their gain was $1800. How much should each one receive?
A's capital, $2500 for 4 mo.= $10000 for 1 mo.
= $34000 for 1 mo.
= $26000 for 1 mo.
o, or f/, of $1800 = $1020. Bis gain – 26000
60000, or 36, of $1800 = $780. Test: $1020 + $780 = $1800, total gain.
8. M and N formed a partnership for 2 years. M put in $ 6100; N put in $3600 and at the end of 6 months added $ 1400. Their settlement at the end of 2 years showed $7956 profits. How should it be divided ?
9. R and S began business as partners April 1, 1904, each investing $5000. On July 1, 1904, they took in T, with $6000. They dissolved partnership January 1, 1905, sharing a profit of $3150. Find each one's share.
10. A, B, and C formed a partnership for 3 years. A put in $10000, B $8000, and C $6000. A withdrew $2000 at the end of 18 months. They dissolved partnership at the end of 2 years with a loss of $ 4750. As nothing could be collected from C, what proportionate share of the loss should A and B pay?
PROBLEMS FOR ORAL AND WRITTEN
1. Two properties are valued at $1000; of the value of the first equals of the value of the second. Find the value of each.
2. At a certain election 1080 votes were cast for A and B;
of the votes cast for A equaled of those cast for B. How many votes were cast for each candidate?
3. A real estate dealer paid $7200 for two city lots; & of the cost of the first lot equaled % of the cost of the second. How much did each cost ?
4. A mill and machinery cost $27000; of the cost of the mill equaled of the cost of the machinery. How much did the machinery cost ?
5. What per cent of a day are 12 hours ? 6 hours ? 36 hours?
6. of Frank's money equals of Henry's, and Frank has $3 more than Henry. How much has each?