Add the following:

26. 5.2x+.05 y −2.1 z, —.6 x — .5 y +.1 z, 3.5 x + .7 y − .5 z.

27. 2x2-5+8x, 2 - 4 x, 17 — x − x2.

--

28. 3a-7b, -8c+4d-8e, 7a+6e+9c-5d+8b. 29. 1.34 m - 7.6 n.397 p, -81.7 p-9.4 m - 8.7 n,

9.76 m +4.33 p + 9.3 n.

30. 41.6q43.1 x + 37.8 y, .09 y 5.37 x

31. .3x2+.1 y2 - .3 yz - .1 z2, .2 xy.3 y2+.3 yz, --.4x2.2xy + .1 y2+.1 x2.

32. Solve 3x+2x+5+9=27 +(-3).

33. Solve 7x+(−3 x)+(-x)=5+(-3)+12.

34. Find the sum of five numbers, the first number being 2x and each succeeding number being 3 a greater than the preceding.

35. If a passenger ticket costs a cents a mile and it costs 4 cents to carry a bicycle each 25 miles, how much is the cost of both for 250 miles?

36. Through how many degrees of longitude does a ship sail in going from · 18° to + 37° ?

37. The oldest known mathematical manuscript was written about 1700 (1700 B.c.). How long ago was it written?

38. A merchant's capital was diminished by $1400 and then amounted to $4500. What was his capital at first?

SUGGESTION. Let x = number of dollars at first.

39. At a certain election A received 113 more votes than B. The number of votes cast for both was 847. How many votes did each receive?

40. A rectangular field is twice as long as it is wide and its perimeter is 360 rods. Find the length and the width of the field.

41. A ball team played 20 games and won three times as many as it lost. How many games were won and how many were lost?

SUGGESTION. Let x = number of games lost.

How

42. A boy paid x cents for a bat, twice as much for a ball, and 20 cents less for a mask than for both ball and bat. much did each cost him if he spent $2.20 all together?

SUGGESTION. Change $2.20 to 220 cents.

43. The larger of two numbers is three times the smaller and their sum is 84. Find the numbers.

44. The larger of two numbers exceeds the smaller by 10, and the sum of the two numbers is 94. Find the numbers.

45. The girls in a certain high school outnumbered the boys by 122. The entire enrollment was 2742. How many boys were there in the school?

46. A woodworking class spent $32.50 more for jack planes than for try-squares. If both tools together cost $50, find the cost of each kind.

47. One farmer by spraying his potatoes raises 30 bushels more on an acre than his neighbor. If both together raise 400 bushels, how many bushels does each raise?

48. In 1910 Jerry Moore of South Carolina won a prize in a boys' corn raising contest. In 1913 Walker Dunson of Alabama raised 4 bushels more corn on an acre than Jerry Moore's record yield. The total yield on the two acres was 460 bushels. How many bushels did each raise?

49. In 1914 the Allred boys, Luther, Clarence, Elmer, and Arthur, of Georgia, raised on four one-acre plots of land 824 bushels of corn. Clarence raised 10 bushels more than Elmer and 7 bushels less than Luther, while Arthur raised 43 bushels less than Elmer. How many bushels did each raise?

IV. SUBTRACTION

SUBTRACTION OF LIKE MONOMIALS

ORAL EXERCISE

88. 1. Define subtraction. (§ 42.)

2. State the rule for subtracting signed numbers. (§ 44.)

Subtract the following:

3. 3-4; 7-8; 10-15.

4. 3-(-4); 9-(-15); 4 -(— 4).

89. From the examples of § 88 we derive the following rule:

To subtract a monomial from a like monomial, change the sign of the subtrahend and add the resulting number to the minuend. (See §§ 42 to 44.)

The student should change the sign mentally.

4.5r-(-7r)=2r.

Add +7r to - 5r. Let the student check the result.

25. The minuend is 0 and the subtrahend is 3x. What

is the difference?

26. The minuend is What is the subtrahend?

27. The subtrahend is

3. What length remains if 10 feet are cut from a rope 32 feet long? if x feet are cut from a rope 32 feet long? if b feet are cut from a rope a feet long?

4. How much have you left if you have 16 cents and spend 7 cents? if you have 16 cents and spend x cents? if you have a cents and spend x cents?

5. If you throw a stone vertically upward h feet, how high is it after it has fallen d feet? How high is the stone if

h = 62 and d = 21?

6. If the enrollment in a class is m girls and n boys and there are x girls and y boys absent, what is the attendance? 7. How are unlike monomials added?

92. To subtract a monomial from an unlike monomial, change the sign of the subtrahend and add the resulting number to the minuend.

EXAMPLES

1. Subtract 2 a from 3x.

The subtrahend when its sign is changed becomes — 2 a; adding this to 3x gives 3x – 2 a.

The result may be checked as usual, 3x-2a + 2a = 3x.