of A's

15. A and B have together 83 sheep; flock, increased by 8 sheep, is equal to B's flock; how many sheep has each?

16. If 10 cents be taken from of Mary's money, the remainder will be equal to Susan's; the girls, together, have 39 cents; how many cents has each? 17. Homer has 3 marbles more than Silas, and of Homer's marbles equal of Silas's; how many has each ?

100. 1. One man will drink a gallon of beer in 3 days; another will drink a gallon in 4 days; how long will a gallon last both of them?

2. Julia can do the washing in 7 hours; with Jane's assistance she can do it in 4 hours; in what time can Jane do it?

3. Two boys can pitch a quantity of hay in 5 hours; the first can do it in 9 hours; in what time can the second do it?

4. A cistern can be emptied by 2 pipes in 3 hours, but 1 pipe will empty it in 74 hours; in how many hours will the other empty it?

5. A can make a vest in g of a day, B in , and C ing of a day; how many more vests can A and B make in a day than C can?

6. Susan can knit a pair of mittens in g of a day, and Sarah can knit a pair in & of a day; how many pairs can both knit in a day?

7. What part of a day must Sarah assist Susan that Susan may complete 2 pairs?

8. What part of a day must Susan assist Sarah that Sarah may complete 3 pairs?

9. Jason can hoe 10 rows of corn in of an hour, and Jesse can hoe them in g of an hour; in what time can both together hoe them?

10. In what time can Jason hoe what remains

after Jesse has hoed

11. In what time

an hour?

can Jesse hoe what remains

after Jason has hoed of an hour?

12. How many rows can both hoe in 1 hour?

13. A and B can clear a field in 15 days; with the help of C they can do it in 9 days; in how many days can C do it?

14. A and B can dig a well in 6 days, A and C in 8 days, and B and C in 9 days; in how many days can each dig it, working alone?

15. In how many days can they do it working together?

16. Patrick, Peter, and Philo can dig 40 rods of ditch in 10 days; Patrick and Peter can do it in 15 days; Peter and Philo can do it in 13 days; in how many days can Patrick and Philo dig 28 rods?

17. How long will it take each man to dig 30 rods? 18. Henry and Harlan can cut a field of corn in 63 days; Harlan's day's work exceeds Henry's by of Henry's; in how many days can each cut the field?

19. Three men can do a piece of work in 10 days; the first does as much as the second, the third does as much as the first and second; in how many days will each do it?

20. In how many days will the first and second do it?

21. In how many days will the first and third do it? 22. In how many days will the second and third do it?

23. A, B, and C can do a piece of work in 8 days; B and C can do it in 12 days, and A and B in 10 days; in how many days can each, working separately, do it?

24. A cistern can be discharged by 3 pipes in 4 hours; the first and second pipes will discharge it in

8 hours; the first and third in 6 hours; in what time will each pipe discharge it?

25. Three men can trench a field in 10 days; A and B can do it in 20 days; B and C can do it in 15 days; in how many days can A and C trench the same field?

26. A barrel of flour would last a brother, sister, and servant 30 days; when the brother was absent it would last 60 days; when the sister was absent it would last 45 days; how long would it last the sister after all had used from it 20 days?

101. 1. Benjamin, meeting some beggars, gave each of them 5 cents; had he given them 7 cents apiece, it would have taken 8 cents more; how many beggars were there?

ANALYSIS. Since 2 cents was the increase paid to 1 beggar, and 8 cents the increase paid to all, there were as many beggars as 2 is contained times in 8, which is 4 times. Therefore, &c.

2. Edward gave 6 plums to each of his playmates, and had 9 remaining; had he given each of them 8, he would have had but 1 left; how many playmates had he?

3. Three times a certain number is 15 less than 6 times the same number? what is the number?

4. Susan, purchasing calico, found that if she took that at 8 cents a yard she would have 11 cents left; but if she took that at 12 cents a yard she would need 17 cents to pay for it; how many yards did she want?

5. 4 times a number is 15 less than 6 times the same number; what is the number?

6. John, being asked how many marbles he had, replied," of them exceed of them by 4." How many had he?

7. 5 times a number is 21 greater than 33 times the same number; what is the number?

8. If 24 chestnuts be divided among some boys, giving 4 apiece to of them, and 2 apiece to the others, how many boys are there?

ANALYSIS. Since one boy received 4 chestnuts as often as another received 2 chestnuts, 2 boys received 6 chestnuts; there were as many times 2 boys as 6 is contained times in 24, which is 4 times, and 4 times 2 boys are 8 boys. Therefore, &c.

9. Mary gave her chickens 26 grains of corn; of them had 5 grains each, the others but 3 each; how many chickens had she?

NOTE. The above gives the following question:

10. 5 times of a certain number, plus 3 times of the same number, is 26; what is the number?

11. A class received 29 merit marks; of them received 5 apiece, of the remainder 3 apiece, 3 of the remainder 2 apiece, and the rest 1 apiece; how many scholars in the class?

12. 26 melons were stolen, of the party getting 4 cach, the rest 3 apiece, except 2, who obtained but 2 apiece; how many were there in the party?

Since

ANALYSIS. Had the last 2 obtained 3 each, there would have been 28 melons; then 4 times of a number, plus 3 times of the same number, or 1, would equal 28. 28 is of a number, 4 of 28, or 4, is, and 4 is times 4, or 8. Therefore, &c.

of 2

13. 4 times of a number, plus 3 times the same number, is equal to 28 plus 5; what is the

number?

14. Henry said that 4 years more than of his age, increased by 5 times of it, and that sum by 4 times of his age less 4, would make the sum 50 years; how old was he?

15. A drover paid $5 a head for of his flock, $4 a head for as many more, $3 a head for of the remainder, and $2 a head for the rest; the flock cost $115; how many sheep had he?

16. A grocer received $10 for a lot of baskets; for of them he had 6 dimes each, for of the remainder plus 3, 4 dimes each, for of the rest plus 2, 3 dimes each, and for the rest 2 dimes each; how many baskets did he sell?

17. 5 times Henry's age is 3 more than 4 times of it increased by 6 times of it; how old is he?

ANALYSIS. 5 times Henry's age equals, 4 times of & it, plus 6 times of it, equals, and less equals of it, which, according to the conditions of the question, is and 3 is of 3 times 3, or 9. Therefore, &c.

3;

of

18. 6 times a number is 4 less than 7 times it, plus 5 times of the same number; what is the number?

19. Bridget, wishing to get a certain number of pounds of meat, found, if she took beef at 5 cents, she would have 4 cents left; if pork at 7 cents, she had not money enough to pay for it; and therefore she took of the quantity in beef, the rest in pork, and paid for it; how many pounds did she get?

20. Four times a number is 6 greater than 5 times of the same number; what is the number?

21. A farmer, wishing to buy a flock of sheep, found, if he paid $2 a head, he would have $60 left; if he paid $5 a head, he had not enough to pay for them; if he took the number at each price, he could just pay for them; how many sheep would his money buy?

22. Twice of a number equals the number plus 8; what is the number?