Had he bought 7 such tops, he would have had but 1c. left. How much were the tops apiece? 11. A lady gave each of her children $3, and had $9 left in her purse. Had she wanted to give each $5, she would have needed $5 more. How many children had she? 12. Horatio is 14 years older than Valorus, and to gether they are 41. How old is each? 13. The difference of two numbers is 10, their sum is 28; what are the numbers ? 14. What two numbers are those, whose sum is 125, and their difference 25 ? SECTION 69.-1. A hound, running after a fox, gains 20 rods on him every minute. If the fox has half a mile the start, how long before he will be caught? 2. A deer is of a mile before a hound, and every minute the deer runs 60 rods, and the hound 70. How long will it be before the deer is overtaken ? 3. A policeman runs 5 rods to a thief's 4. The thief has 10 rods the start; how far will the policeman run before he catches the thief? MODEL. If the policeman runs 5 rods to the thief's 4, he gains 1 rod on every 5 he runs; and, to gain 10 rods, he will have to run as many times 5 rods as 1 rod is contained times in 10 rods, or 10. 10 times 5 is 50. Ans. 50 rods. 4. How far will the thief mentioned in the last Example run before he is caught? 5. A hare is 25 leaps in advance of a hound, and takes 4 leaps to the hound's 3, but 1 leap of the hound equals 14 leaps of the hare. How many leaps will each take before the hare is caught? 6. A train of cars is 10 miles behind a stage. If the cars go 5 times as fast as the stage, how many miles, &c., will the stage go before it is overtaken ? 7. At what time between 2 and 3 o'clock are the minute and hour hand of a watch together? MODEL. The minute and hour hand are together at 12 o'clock. In the course of 12 hours, the minute hand will overtake the hour hand 11 times; to overtake it once, therefore, will require of 12 hours, or 1 hours. When the hands are together between 2 and 3, the minute hand will have overtaken the hour hand twice since 12 o'clock, which will require twice 1 hours, or 2 hours. Ans. 2 hours past 12, or 10 min. 54 sec. past 2. 8. At what time between 3 and 4 will the hour and minute hand of a clock be together? 9. At what time between 7 and 8 will the hands be together? At what time between 9 and 10 ? 10. A person received from his employer $74, under an agreement that he was to board with the latter 40 days, and receive $2.50 a day when he worked, and lose 75c. a day when he was idle. How many days was he idle? MODEL. His pay being $2.50 a day, if he had worked the whole 40 days, he would have received 40 times $2.50, or $100; hence he lost by being idle the difference between $100 and $74, or $26. Each day he was idle he failed to make $2.50, and forfeited 75c. besides, thus losing in all $34. Hence, if he lost $26, he must have been idle as many days as $31 is contained times in $26, or 8. Ans. 8 days. SECTION 70.-1. A contracted to work 36 days for B, on condition that he should receive $2 for every day he worked, and forfeit 50c. each day he was idle. If he received from B $47, how many days was he idle? 2. How many square yards in an oblong surface 7 yards long and 4 yards wide? MODEL. A surface 1 yd. long and 1 yd. wide contains 1 sq. yd.; a surface 7 yd. long and 1 yd. wide, would therefore contain 7 times 1, or 7, sq. yd.; and a surface 7 yd. long and 4 yd. wide contains 4 times 7, or 28, sq. yd. Ans. 28 sq. yd. 3. How many square rods in an oblong field 20 rods by 15 rods? 4. How many sq. yd. in a floor 12 ft. square? 5. At 30c. a square yard, what will it cost to plaster a wall 10 ft. high and 18 ft. long? 6. What will it cost to paint a wall 9 yd. long and 4 yd. high, at 5c. per square foot? 7. How many marble blocks 12 in. square will be needed to pave a walk 3 ft. wide and 20 ft. long? 8. How much yard-wide carpeting will be required to cover a room 18 ft. by 15 ft. ? 9. How much carpeting of a yard wide is required for a room 9 yd. long by 14 ft. wide? 10. How many cubic feet in a box 4 ft. long, 3 ft. wide, and 2 ft. high? MODEL. A box 1 ft. long, 1 ft. wide, and 1 ft. high, would contain 1 cu. ft.; a box, therefore, 4 ft. long, 1 ft. wide, and 1 ft. high, would contain 4 times 1, or 4, cu. ft.; a box 4 ft. long, 3 ft. wide, and 1 ft. high, would contain 3 times 4, or 12, cu. ft.; and a box 4 ft. long, 3 ft. wide, and 2 ft. high, contains twice 12, or 24, cu. ft. Ans. 24 cu. ft. 11. How many cubic yards in a bin 5 yd. long, 2 yd. wide, and 3 yd. high? 12. What is the freight on a box 3 ft. long, 3 ft. wide, and 3 ft. high, at 50c. a cubic foot? 13. What will it cost to dig a cellar 12 feet long, wide, and high, at 60c. a cubic yard? CHAPTER ELEVENTH. PERCENTAGE. SECTION 71.-1. What do the words Per cent. mean? Ans. By or on the hundred. 2. What does 1 Per cent. mean, and how may it be written? Ans. 1 Per cent. means one on every hundred, or 1 hundredth, and may be written 1%. 3. What does 2 Per cent. mean, and how may it be written? Ans. 2 Per cent. means two hundredths (1), and may be written 2%. 12. What per cent. is equal to? ?? equal to??? equal to ??? equal to ??? equal to??? What part is 66% ? What part is 12% ? SECTION 72.-1. If a person loses of his property, what per cent. of it has he left? 2. If a person sells 30% of his sheep, what part of his flock does he retain? 3. How much is 5% of $500 ? MODEL. 5%=150. of $500 is $5, and 150 is 5 times $5, or $25. Ans. $25. 4. How much is 4% of $25? MODEL. 4%=115, or 2. of $25 is $1. Ans. $1. NOTE. It is sometimes best to reduce the fraction to its lowest terms, as in this Example,-and sometimes not, as in the last. The pupil must exercise his judgment. 5. How much is 3% of $175 ? 12. How much is 83% of 27 A.? 10% of $345 ? 25% of $960 ? 40% of $75? |