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1896-6-10
1892-9-25

3-8-15

THE USUAL METHOD.

From the 1896th yr., the 6t the 10th day, subtract the 1891 9th mo., and the 25th day. month as 30 days.

A BETTER METHOD.

From Sept. 25, 1892 to Sept. 25, 1895, is 3 ye
From Sept. 25, 1895 to May 25, 1896, is 8 mo
From May 25, 1896 to June 10, 1896, is 16 daj

NOTE. The two methods will not always produce the same results. possible variation is two days. Find the time from Jan. 22, 1895, to Ma by each method, and compare results. The difference arises from the month as a measure of time is a variable unit-sometimes 28 times 31. The "usual method" regards each month as 30 days; method" counts first the whole years, then the whole months, the remaining. By the "usual method," the time from Feb. 28, 1897 to M is 3 days; by the "better method," it is 1 day.

PROBLEMS.

Find the time by both methods and compare the 1. From March 15, 1894 to Sept. 10, 1897. 2. From March 15, 1894 to Sept. 20, 1897. 3. From May 25, 1895 to Sept. 4, 1898. 4. From May 25, 1895 to Oct. 4, 1898. 5. From June 28, 1894 to Mch. 1, 1898. 6. From June 28, 1894 to May 1, 1898. 7. From Jan. 10, 1892 to Jan. 25, 1898. 8. From Jan. 10, 1892 to Dec. 25, 1898. 9. From April 15, 1893 to Aug. 15, 1898.

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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 income?

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 James's money); 3rd, by the application of the 100 n formula,

= x.

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TO THE TEACHER.-Require the pupils to solve the first f ems in four ways:

(1) Let x = the per cent and solve as the "example" is s (2) Using one hundredth of each base as a divisor and t number mentioned in the problem as a dividend, find the q (3) Find what part the first number mentioned in each pro of the base, and change the fraction thus obtained to hundred 100 n

(4) Apply the formula,

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* The b in problem 6, and in the formula may be thought of as standin

Dase.

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 times 90° degrees.

=

2. Six equal equilateral triangles 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 60°. Six times 60°

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

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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, it 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.

4. Find the amount of $630 from July 1, 1896, 1896, at 7%.

5. Find the amount of $800 from Jan. 1, 1897, 1897, at 6%.

6. If a 60-day bill of $400 is discounted 2% how much ready money will be required to pay th

7. Find the amount of $392 for 60 days (tw at 6%.

NOTE -Observe that $392 is the answer to problem 6. of problem 7, then, is the amount that the goods mention lem 6, would cost at the end of 60 days if the purchaser bo money at 6% to pay for them. Compare this result How much does the purchaser of the bill save by borr money at 6% to pay the bill instead of letting the bill r and then paying $400?

8. Find the cost of goods, the list price being the discounts "50 and 10 off and 2 off for cash."

9. My remuneration for selling goods on a con of 40% amounted to $56.20. How much should for whom the goods were sold receive?

NOTE.-$56.20 is 40% of the selling price of the goods. for whom the goods were sold should receive 60% of the selli When goods are sold on a commission of 40%, what tl receives equals what part of what the employer receives? employer receives is how many times what the agent receive

12. The sum of all the angles of 6 triangles equa many right angles?

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