will give the amount of feeding surface needed in the preceding problem?

7. How many tons of silage are needed to feed 20 cows 200 days, feeding each cow 25 lb. daily? How many cubic feet of silage is this, counting 40 lb. to the cubic foot?

8. What must be the height of a silo with inside diameter 12 ft. to hold the amount of silage found in the preceding problem?

9. A cylindrical silo is made of concrete with walls 6 in. thick. The inside diameter is 14 ft. and the height is 30 ft. How many cubic feet of concrete are required?

10. Show that a cylindrical silo 18 ft. in diameter holds approximately as much as a square silo of the same height and 16 ft. square, inside measurement in each case. Find the difference in the amount of concrete to build one of each form, 30 ft. high, with walls 6 in. thick.

11. A 1:24 mixture of cement, sand, and gravel is used to make the walls of silos. Find the cost of the materials for making the walls of each of the silos in problems 9 and 10 if cement costs 50¢ a cubic foot, sand $1.10 a cubic yard, and gravel $1.10 a cubic yard.

12. A wooden silo is 15 ft. in diameter, outside measurement, and 30 ft. high. Find the cost of the paint, at $1.70 a gallon, for painting the outside, allowing 1 gallon to 250 sq. ft.

13. The silo in problem 12 has a conical roof whose slant height is 11 ft. and the radius of whose base is 9 ft. How many bundles of shingles are required for this roof, allowing 1000 shingles to 100 sq. ft.? A bundle contains 250 shingles.

CHAPTER VI

NEGATIVE NUMBERS

50. Meaning of negative numbers. In playing beanbags a player is allowed so many points for each of the circles into which he throws, but he loses a certain number of points for each throw that misses the board. His first throw counts 8, his second counts 5, his third throw misses the board, losing 10, his fourth counts 5, his fifth counts 6, and his sixth loses 10. In keeping the score the counts for him are marked +, meaning that these numbers are to be added to his score, while the counts against him are marked -, meaning that these numbers are to be subtracted from his score. counts, then, are +8, +5, -10, +5, +6, −10. Find his final score.

His

The number +8 is read "plus 8" or "positive 8." The number - 10 is read "minus 10 or negative 10." What score does the next player make in two throws if his first count is +7 and the next +5? In three throws counting +7, +5, and −10? What score does a player make in four throws counting +8, +6, -10, +2? In two throws counting +8 and -10? In three throws counting +7, −10, +6?

It is easy to measure such scores along a straight line as in Figure 68. Such a line as this is called a number scale.

The counts +7, -10, and +6 may be found by counting to the right for the plus counts and to the left for the minus counts.

Starting at O, OA is +7, AB is -10, and BC is +6. The score after any throw is the distance from the starting point O, to the stopping point after that throw. After the first throw his score is OA, or +7; after the second it is OB, or after the third it is OC, or +3.

-3;

A poor player misses his first throw, counting 10 against him. What is his score then? His second throw goes into the ring counting 5, his third into the ring counting 2, his fourth misses, his fifth counts 4, his sixth counts 1, and his seventh misses. What is his score then? A second player misses his first throw, his second goes into the ring counting 5, his third into the ring counting 2, his fourth misses, his fifth counts 4, his sixth counts 1, and his seventh misses. What is his final score? Show on a number scale his

score after each throw.

The thermometer scale is just such a line for keeping temperature scores. As the heat increases the mercury rises and as the heat decreases the mercury falls. The temperature score is the number of degrees above or below zero at which the mercury stands.

Exercise 55

1. Combine these counts, made in playing a game, and give each player's final score.

2. On a number scale show the score of each player after each throw.

3. On a certain day the temperature started at -8° and readings showed these changes: −2o, −5°, +1°, +3°, +5°, +10°, +3°, +1°, -4°. What was the final temperature? On a number scale show the results of combining the following numbers:

16. In keeping account of business ventures it is customary to call the expenditures minus amounts and the receipts plus amounts. A boy goes into the chicken business with +$15. His account shows the following amounts: -$2; -$1.75; +$.50; +$1; +$3; -$.25. How much has he then?

51. Adding signed numbers. Find the final score of a player whose counts are +8, -10, +5, +2, −6.

Combining +8, −10, +5, +2, and −6 in this way is called adding them, and the result is called their sum.

On the number scale these numbers may be added by beginning at zero and counting 8 spaces to the right, then 10 spaces to the left, then 5 spaces to the right, then 2 more spaces to the right, then 6 spaces to the left. The sum is then the number represented by the distance and the direction from the zero point to the stopping point.

Make a scale and on it find the sum of the following:

Can you make a rule for finding the sum of two numbers having the same sign? Two numbers having unlike signs?

The value of a number without regard to its sign is called its absolute value. Thus, the absolute value of +4, also of -4, is 4.

Rule. To add two numbers having like signs add their absolute values and give their sum the common sign.

To add two numbers having unlike signs find the difference of their absolute values and give this difference the sign of the number having the greater absolute value.

If the sign of a number is omitted, the plus sign is understood. Thus, +8a is often written 8a.