Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

C says to A, I have half as many as you. They then counted their money, and found that they had 70 dollars. How much money had each ?

21. A man had 45 cents; he gave away a certain number, and found that he had four times as many remaining as he gave away. How many did he give away?

22. A boy had 60 marbles; he lost a number of them, and found that he had five times as many remaining as he had lost How many had he lost?

23. A man having a lease for 20 years, found that four times as much of the time had passed as there was to come. How much of the time was yet to come?

How

24. A man having a lease for 30 years, found that five times as much of the time had passed as there was to come. much of the time was yet to come?

SECTION II.

Introductory Lessons.

1. If x stands for the number of miles a man travels in 1 hour, what will stand for the number of miles that he will travel in 2 hours?

Ans. 2 x.

What will represent the number of miles that he will travel in 3 hours? In 4? 5? 6? 7?

2. If 2 x represent the number of miles a man travels in 1 hour, what will represent the number of miles that he will travel in 2 hours? In 3? 4? 5? 6? 7? 8?

3. Two men set out from the same place and travel in opposite directions; the second travels twice as far in an hour as the first. At the end of an hour they are 9 miles apart. How far does each travel in an hour?

Let x represent the number of miles that the first travels in an hour; then 2x will represent the number of miles that the second travels in an hour. Hence they are 3 x miles apart. Consequently, 3 x are equal to 9; but if 3 x are equal to 9, 1 x is equal to of 9, or 3, &c.

4. Two men set out from the same place, and travel in opposite directions; at the end of 3 hours, they are found to be 27 miles apart; and it is known that one has traveled twice as fast as the other. How many miles did each travel per hour?

5. Three men set out to travel at the same time; the first traveled twice as fast as the second, and the third three times as fast as the second. At the end of 4 hours, the number of miles they had all traveled, added together, amounted to 48. How far did each one travel in an hour?

6. Two men built 90 rods of fence in 3 days. The second built twice as many rods per day as the first. How many rods. did each build per day?

7. A man bought 3 oxen, 4 cows and 6 calves for 260 dollars. He paid twice as much for an ox as he did for a cow, and twice as much for a cow as he did for a calf. How much did he give for each ?

S. A man bought some barrels of flour for 132 dollars, onehalf at 5 dollars per barrel, and the other half at 6 dollars per barrel. How many barrels did he buy?

Let x represent half the number of barrels. Then if they were 1 dollar per barrel, x would represent the number of dollars they would come to, for there would be just as many dollars as barrels. If they were 2 dollars per barrel, they would come to 2x dollars, for they would come to twice as many dollars as barrels, &c. Hence x barrels, at 5 dollars per barrel, would come to 5 x dollars; and x barrels, at 6 dollars per barrel, would come to 6 x dollars; therefore, 5 x and 6 x, or 11x, are equal to 132. Consequently, x would be equal to TT of 132, or 12.

9. A man bought the same number of bushels of wheat, and barrels of flour; the wheat at 1 dollar per bushel, and the flour at 5 dollars per barrel. The whole came to 96 dollars. How many bushels of wheat and how many barrels of flour were there?

10. Two men built 100 rods of fence; one built 4 rods per day, and the other 6. How many days did they work?

11. Two men set out from two towns 50 miles apart, and traveled till they met. One traveled 7 miles per hour, and the other 3. How long before they met? If the towns were 60 miles apart, how long before they would meet? If 70, how. long? If 80? 90? 100?

12. If one traveled 6 miles per hour, and the other 5, how long before they would meet, if the towns were 22 miles apart? If 33 miles apart, how long? If 44? 55? 66?

77?

88 ?

99?

13. A man bought an equal number of apples, oranges and pears. The apples at 3 cents a piece, the oranges at 4, and the pears at 5, for 96 cents. How many of each kind did he buy?

14. A man bought three times as many pairs of shoes as boots; both came to 108 dollars. The shoes at 2 dollars a pair, and the boots at 6 dollars a pair. How many pairs of each did he buy?

15. A man bought twice as many apples as oranges; both cost 70 cents. The apples at 4 cents a piece, and the oranges at 6 cents. How many of each did he buy?

16. Three men set out, at the same time, to travel; one went 3 miles per hour, another 4, and the third 5. After traveling a number of hours, it was found that they had traveled altogether 132 miles. How many hours had they traveled?

17. A man bought some sugar, coffee and tea, an equal number of pounds of each. The sugar at 10 cents per pound, the coffee at 15, and the tea at 30. The whole came to 220 cents. How many pounds of each did he buy?

18. A man bought at market twice as many chickens as turkeys, for 120 cents; the chickens at 10 cents a piece, and the turkeys at 40 cents a piece. How many of each did he buy?

19. There is a number such, that four times the number multiplied by 5, and six times the number multiplied by 3, give together 76. What is the number?

SECTION III.

Introductory Lessons.

1. Two boys had 24 marbles, and one had 4 more than the other. How many had each ?

Let x represent what one had; then x and 4 must represent what the other had. Then 2x and 4 are equal to what both had therefore, 2 x and 4 are equal to 24. If 2 x and 4 are equal to 24, 2 x must be equal to 4 less than 24, since 4 added to 2x makes 24; consequently, 2 x are equal to 20, and 1 x must be equal to of 20, or 10. x and 4 are 14.

One boy had 10, and the other 14.

2. Two boys had 28 cents, and one had 4 more than the other. How many had each?

3. Two boys had 36 cents, and one had 6 more than the other. How many had each?

4. Two numbers make 27, and one is 3 more than the other. What are the numbers?

5. Two numbers make 48, and one is 8 more than the other. What are the numbers ?

6. Two numbers make 35, and their difference is 3. What are the numbers ?

7. The difference between two numbers is 5, and their sum is 55. What are the numbers ?

8. Two numbers are together equal to 34; one is twice as much as the other, and 4 more. What are the numbers ?

Let x represent one of the numbers; then 2 x and 4 must represent the other; and 3 x and 4 will represent the sum of the two numbers. Hence 3 x and 4 must be equal to 34, &c.

9. One number is twice as much as another, and 6 more ; and the two together make 66. What are the numbers?

10. Two men bought a horse for 95 dollars; one paid twice as much as the other, and 5 more. What did each pay?

11. A man bought a hat and a coat for 35 dollars; the coat cost twice as much as the hat, and 5 dollars more. How much did each cost?

12. Divide 100 into two such parts, that one shall be twice as much as the other, and 10 more.

13. Divide 30 into two such parts, that one shall be twice as much as the other, and 6 more.

14. Two numbers added together make 60; one is three times as much as the other, and 12 more. What are the numbers?

15. Two numbers added together make 16; one is four times as much as the other, and 6 more. What are the numbers ?

16. Two men bought a carriage for 86 dollars. One paid five times as much as the other, and 26 more. What did each

pay?

17. Divide the number 37 into three parts, so that the sec ond may be 3, and the third 4, more than the first.

Let x represent the first part; then x and 3 must represent the second part, and x and 4 the third part. Hence 3 x and 7 represent all the parts: consequently, 3x and 7 are equal to 37, 3 x are equal to 30, x equal to 10.

18. Divide the number 100 into three parts, such that the second may be 3 more than the first, and the third 4 more than the first.

19. Divide 61 into three such parts, that the second may be 3 more than the first, and the third 1 more than the second.

20. Three men paid 65 dollars for a horse; the second paid 5 more than the first, and the third 10 more than the second. How much did each pay?

21. Three men traveled altogether 127 miles. The second traveled 10 miles farther than the first, and the third 17 farther than the second. How far did each travel?

22. Divide 60 into three such parts, that the second shall be twice as much as the first, and the third 20 more than the second.

23. A man had three flocks of sheep; in the second flock he had twice as many as there were in the first, and 12 more; and in the third he had 8 more than there were in the second. In all he had 102 sheep. How many had he in each flock?

24. A man had six sons, to whom he gave 120 dollars; giving each one 4 dollars more than his next younger brother. How many dollars did he give to each?

25. What will represent twice as much as x and 4?

Ans. 2 x and 8.

26. What will represent three times as much as x and 8? Four times as much as x and 14? Three times as much as 2 x and 3?

as

27. What will represent as much as 2x and 4? much as 3x and 9? as much as 8 x and 16? as much as 20 x and 25?

28. A man paid a debt of 29 dollars, at three different payments; at the second, he paid 3 dollars more than at the first, and at the third twice as many as at the second. How much did he pay each time?

29. Four men, A, B, C and D, have 116 dollars between them. A says to B, I have twice as much as you, and 12 more; says C to A, I have half as much as you; but says D, I have as much as all of you together. How many has each?

30. A man, driving his geese to market, was met by another, who said, Good morning, master, with your hundred geese.

B

« ΠροηγούμενηΣυνέχεια »