2. The following payments were made on a $650 note, bearing 7% interest and dated April 20, 1901:

3. A note of $2800, dated Feb. 23, 1900, and bearing 7% interest, carried the following indorsements:

1. Joseph had 45¢ and he earned 15¢ more selling oranges. How many cents had he then? (Answer by indicating the operation you perform, thus: 45¢ + 15¢.)

2. William had x marbles and Harold gave him y marbles. How many marbles had he then?

3. A cow gave x lb. of milk at the morning milking and y lb. at the evening milking. How many pounds did she give at both milkings?

4. James earned 80¢ selling papers on Saturday and spent 45¢ of his earnings. How many cents did he save?

5. During July a boy earned m dollars and spent s dollars. How many dollars did he save?

6. Helen bought 15 pencils at 3¢ apiece. How much did she pay for all?

7. Elizabeth took x music lessons during February at y dollars per lesson. What was the cost of her lessons for the month?

8. A thermometer rose A° on one day and 5 times as much the day following. How much did it rise on the following day?

9. The area of a rectangular lot is 63 sq. rd. and the length of one side is 9 rd. How long is the other side?

10. The area of a rectangle is x square inches and the length of one side is y inches. How long is the other side?

11. How many lots each of b ft. frontage can be made from a frontage of a feet?

12. An orange boy earns a cents on Wednesday, three times as many cents on Thursday, and as many cents on Friday as on Wednesday and Thursday together. On all three days he earns 80¢. How much does he earn on Thursday? On Friday?

NOTE. In all such problems use the equation. We have a + 3a

13. The altitude of a rectangle is x in. and the base is 3x in. How long is the perimeter? What is the area of the rectangle?

14. 4a means 4 X a. Compare the values of a × 4 × a and 4 × a X a. How is a X a written? How is 4 Xa xa. Xa written? Ans. 4a2.

15. The mercury stood at x degrees at 2 P.M. and fell 3° during the next hour. The reading at 3 P.M. was 25°. What was the reading at 2 P.M.?

16. The mercury stood at 12° at 8 A.M. During the next two hours it rose x degrees. What was the thermometer reading at 10 A.M.? If it had fallen y degrees, what would have been the reading at 10 A.M.?

17. The thermometer read 28°, the mercury fell x degrees, then 3x degrees, and then rose 6x degrees, when the reading was 32°. What was the number of degrees in each of the three changes?

18. James paid $x for a hat and twice as much for a coat. He paid $4.50 for both. What did he pay for each?

19. I paid $30 for a bicycle and sold it for $x. How much did I gain?

20. I paid of what I gained for a coat. How much did I pay for the coat?

21. Louis had x apples and ate y of them. How many did he have left?

22. Henry had 7a papers and sold 4a of them. How many did he have left?

23. I walked x miles due south one day and y miles due north the next day. How far was I then from my starting point?

24. A man rows a boat downstream at a rate that would carry his boat a miles per hour through still water, and the current alone would carry him down b miles per hour. How far will he go in 1 hour?

25. A man walks from rear to front through a railway coach 3 mi. per hour, and the coach is running at the same time a mi. per hour. How fast does the man pass the telegraph poles along the track?

26. How fast does he pass them if he walks from front to rear?

27. Mary had a pencils and sold them at 5¢ apiece. How many cents did she receive for them?

28. James sold x oranges at a cents apiece. How many cents did he receive for them?

29. A dealer sold a wagons for 40a dollars. What was the price per wagon?

30. A farmer paid x dollars for 15 A. of land. How much did he pay per acre?

31. The area of a rectangle is m sq. rd. and it is 7 rd. long. How wide is the rectangle?

32. A township is x m. square and contains 36 sq. mi. What is the value of x? What does x represent?

33. Helen bought x dolls at 10¢ apiece and y yd. of muslin at 8¢ a yard. How many cents did she pay for both?

34. James had m cents and earned c cents more. He invested all his money in papers at 3¢ apiece. How many papers did he buy?

35. He sold his papers at 5¢ apiece. How much did he receive for the papers? How much did he gain?

36. The base of a triangle is x ft. and the altitude is y ft. What is the area in square inches?

37. The area of a triangle is x sq. ft. and the base is 6 ft. long. What is the altitude?

38. A parallelogram has a base (x + y) in. long, and is 6 in. high. What is the area? Express this answer in two ways and make an equation by writing the two expressions equal. Why are the two expressions equal?

39. A parallelogram having an altitude of x in. and a base of 2x in. has an area of 32 square inches. Find the lengths of the altitude and base.

§130. Uses of the Equation.

1. If each brick weighs 7 lb. and there are 10 bricks in the bucket (Fig. 1), with how many pounds of force does the bucket pull downward on the rope, the bucket itself weighing 5 pounds?

2. If we denote the number of pounds of force with which the man pulls downward on the rope to balance the bucket by p, write an equation showing the number of pounds in p, the 5-lb. bucket being loaded with 10 bricks.

FYL

FIGURE 2

FIGURE 1

3. A horse is raising a 10-ft. steel I-beam weighing 30 lb. for each foot of length. (See Fig. 2.) If the force the horse must exert to hold the beam suspended in the air be denoted by F, write an equation showing the number of pounds in F.

4. A wagon weighing 1800 lb. is loaded with 3 T. of coal. When it is being drawn over ordinary pavement it pulls backward on the traces of the team with a force of

as many pounds as there are pounds in the entire weight of the coal and wagon. If the force exerted by the moving team is F lb., write an equation showing the number of pounds in F.

5. Write an equation showing how many pounds each horse draws if both draw with equal force.

These problems show how the equation may be used in solving simple problems of mechanics; and we need to learn the laws upon which the use of the equation is based.