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248. ALGEBRA APPLIED TO PROBLEMS IN PERCENTAGE.
the number sought.
100 Multiplying by 100,
7500, Dividing by 15,
1. 56 is 2 per cent of what number? 2. 45 is 5 per cent of what number? 3. 60 is 12 per cent of what number? 4. 37 is 4 per cent of what number? 5. 53 is 8 per cent of what number? 6. n is r per cent of what number? Let
x = the number sought.
7. James has $54.20, and James's money equals 40 per cent of Henry's money.
How much money has Henry ? 8. Mr. Williams's annual expenses are $791.20; this is 92
per cent of his annual income. How much is his annual
9. Mr. Randall has 450 sheep; these equal 125 per cent of Mr. Evans's sheep. How many sheep has Mr. Evans ?
* TO THE TEACHER.-Encourage pupils to solve the 7th, 8th, and 9th problems in three ways: 1st, by the method given above; 2nd, arithmetically (Prob. 7– Henry's money equals 100 40ths of Janies's money); 3rd, by the application of the
100 n formula,
249. ALGEBRA APPLIED TO PROBLEMS IN PERCENTAGE.
60 is what per cent of 75 ?
the per cent (number
1. 180 is what per cent of 200?
the per cent.
= n. 100
100 Multiplying by 100,
100 n Dividing by b,
of b or,
TO THE TEACHER.—Require the pupils to solve the first five prob. lems in four ways:
(1) Let x = the per cent and solve as the "example” is solved.
(2) Using one hundredth of each base as a divisor and the other number mentioned in the problem as a dividend, find the quotient.
(3) Find what part the first number mentioned in each problem is of the base, and change the fraction thus obtained to hundredths.
100 n (4) Apply the formula,
* The b in problem 6, and in the formula may be thought of as standing for the base.
Geometry. 250. SOME INTERESTING FACTS ABOUT SQUARES, TRIANGLES, AND HEXAGONS.
1. Four equal squares may be so joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 90°. Four tinies 90°
degrees. 2. Six equal equilateral triangles may be se joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 60°. Six times 60o = degrees.
NOTE.-Cut from paper 6 equal equilateral triangles and join them as shown in the figure.
3. Three equal hexagons may be so joined as to cover all the space about a point. Each angle whose vertex is at the central point of the figure is an angle of 120°. Three times 1200 degrees.
NOTE.—Cut from paper 3 equal hexagons and join them as shown
in the figure.
4. Since every regular hexagon may be divided into six equal equilateral triangles, * as shown in the figure, .t follows that the side of a regular hexagon is exactly equal to the radius of the circle that circumscribes the hexagon.
* See Observation, page 149.
251. MISCELLANEOUS REVIEWS. 1. Find the interest of $250 from Sept. 5, 1896, to Jan. 17, 1898, at 6%.
2. Find the amount of $340 from April 19, 1895, to Oct. 1, 1896, at 6%.
3. Find the amount of $500 from May 20, 1897, to Feb. 28, 1898, at 5%.
4. Find the amount of $630 from July 1, 1896, to Nov. 1, 1896, at 7%.
5. Find the amount of $800 from Jan. 1, 1897, to Jan. 25, 1897, at 6%.
6. If a 60-day bill of $400 is discounted 2% for cash, how much ready money will be required to pay the bill?
7. Find the amount of $392 for 60 days (two months) at 6%.
NOTE.-Observe that $392 is the answer to problem 6. The result of problem 7, then, is the amount that the goods mentioned in problem 6, would cost at the end of 60 days if the purchaser borrowed the money at 6% to pay for them. Compare this result with $400. How much does the purchaser of the bill save by borrowing the money at 6% to pay the bill instead of letting the bill run 60 days and then paying $400 ?
8. Find the cost of goods, the list price being $46, and the discounts “ 50 and 10 off and 2 off for cash."
9. My remuneration for selling goods on a commission of 40% amounted to $56.20. How much should the man for whom the goods were sold receive?
Note.—$56.20 is 40% of the selling price of the goods. The man for whom the goods were sold should receive 60% of the selling price When goods are sold on a commission of 40%, what the agent receives equals what part of what the employer receives? What the employer receives is how many times what the agent receives?
10. The sum of all the angles of 6 triangles equals how many right angles?
252. When a man borrows money at a bank he gives his note for a specified sum to be paid at a specified time and he receives therefor, not the sum named in the note, but that sum less the interest upon it from the time the note is given to the bank officials to the time the note is due.
253. The acceptance of a note by the bank officials and the payment of a sum less than it will be worth at maturity* is called "discounting the note."
254. The proceeds of a note is the sum paid for it. rule, the notes discounted at a bank are those which bear no interest, and the date of discounting is usually the same as the date of the note, though not necessarily so.
EXAMPLE Find the discount and proceeds of the following: $800
JACKSONVILLE, ILL., Jan. 10, 1898. Sixty days after date I promise to pay James Rice or order, eight hundred dollars, value received.
ARTHUR WILLIAMS. Discounted at 6%, Jan. 10, 1898. From the date of discount to the date of maturity it is 60 days. Interest of $800 for 60 days $8.00.
Proceeds of note = $800 – $8 $792.
Observe that the bank receives the interest on $800 for two months at 6% for the use of $792 for two months. The actual rate of interest is therefore a little more than the rate named.
* The date of maturity is the day upon which the note is legally due.