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14. Says A to B, I have 5 times as much money as you; yes, says B, but if you will give me $17, I shall have 7 times as much as you. How much had each?
15. Two men, A and B, commenced trade ; A had $500 less than 3 times as much money as B; A lost $1500, and B gained $900, then B had twice as much as A. How much had each at first ?
16. From each of 15 coins an artist filed the value of 2 shi lings, and then offered them in payment for their original value, but being detected, the whole were found to be worth no more than $145. What was their original value ?
17. A boy had 41 apples, which he wished to divide between three companions, as follows ; to the second he wished to give twice as many as to the first, and three apples more; and to the third he wished to give three times as many as to the second, and 2 apples more. How many must he give to each ?
18. A person buys 12 pieces of cloth for 149 crowns : 2 are white, 3 are black, and 7 are blue. A piece of the black costs 2 crowns more than a piece of the white, and a piece of the blue costs 3 crowns more than a piece of the black. Required the price of each kind.
See example 4th of this Art.
19. A man bought 6 barrels of flour and 4 firkins of butter ; he gave $2 more for a firkin of butter, than for a barrel of flour; and the butter and flour both cost the same sum. What did he give for each?
20. A grocer sold his brandy for 25 cents a gallon more than his wine, and 37 gallons of his wine came to as much as 32 gallons of his brandy. What was each per gallon?
21. A man bought 7 oxen and 36 cows ; he gave $18 apiece more for the oxen than for the cows, and the cows came to three times as much as the oxen wanting $3. What was the price of each !
22. A man sold 20 oranges, some at 4 cents apiece, and some at 5 cents apiece, and the whole amounted to 90 cents. How many were there of each sort ?
If he had sold 13 at 5 cents apiece, then the number sold at 4 cents apiece would be 20--13, or 7.
In the same manner, if he sold 5 oranges at 5 cents apiece, then he sold 20 x oranges at 4 cents apiece. 2 oranges at 5 cents apiece would come to 5 x cents, and 20 x oranges at 4 cents apiece would come to 4 times 20. x cents, which is 30–4 x cents. These added together must make 90 cents, therefore
5x + 30 - 4x = 90 By transposing 80 and uniting terms, r = 10 at 5 cents.
Ans. 10 of each sort. 23. A man dying left an estate of $2500 to be divided between his two sons, in such a manner, that twice the elder son's share should be equal to three times the share of the second. Required the share of each.
Let x denote the younger son's share.
By the conditions, 3 x — 5000
ū = 1000
Ans. Elder son $1500, younger son $1000. 24. Two robbers, after plundering a house, found they had 35 guineas between them; and that if one of them had 4 guineas more, he would have twice as many as the other. How many had each?
25. A man sold 45 barrels of flour for $279 ; some at $5 and some at $8 per barrel. How many barrels were there of each sort?
26. A man sold some oxen and some cows for $330; the whole number was 15. He sold the cows for $17 apiece, and the oxen for $32 apiece. How many were there of titch sort :
27. After A had lost 10 guineas to B, he wanted only 8 Qvineas in order to have as much money as B; and together itey had 60 guineas. What money had each at first ?
Let x be the number of guineas A had.
-x will be the number B had. A lost 10 to B, therefore A's is diminished by 10, and B's increased by 10, which makes A’s x - 10, and B's 70
By the conditions, r- 10 +8=70 --X
x = 36 = what A had.
60-_ 36 24 = what B had. 28. Divide the number 197 into two such parts, that four times the greater may exceed five times the less by 50.
29. Two workmen were employed together for 50 days, at 5 shillings per day each. A spent 6 pence a day less than B did, and at the end of the 50 days he found he had saved twice as much as B, and the expense for two days over.
What did each spend per day?
Let w denote what A spent per day (in pence).
Then 60 — (5s. being 60d.) will be what he saved per day.
B saved 6d. less than A.
By the conditions A saved 2 x more than twice what B
50 = what A spent. 50 +6 = 56
56 = what B spent.
V. 1. Two persons talking of their ages, A said he was 25 years older than B, and that one half of his age was equal to three times that of B wanting 35 years. What was the age of each?
Let x denote the age of B.
of A will be x + 25. 1 of x + 25 is expressed *+ 25
Hence we have
30—35 = x+ 25
Multiplying by 2,
= 25+ 70
age. x + 25 = 44 = A's age.
Note. Since 1 of x + 25 is 3 x 35, x + 25 must be twice 32-35.
2. Two men talking of their horses, A says to B, my horse is worth $25 more than yours, and of the value of my horse is equal to of the value of yours. What is the value of each ? Let x denote the value of B's horse. Then the value of A's will be x +25.
3x + 75 of x + 25 is
is 3 times as much, that is 5
3 x + 75 By the conditions,
X + 25
Multiplying by 5,
= 3x + 75
3 x = 300
Ans. A's $125, B's $100. Proof. The first condition is evidently answered. With regard to the second, of 125 is 75, and of 100 is 75.
3. Two men talking of their ages, one says, my age of yours, but in twenty years from this time, if we live, it will be of yours. Required the age of each. Suppose the age of the elder
x. Then the younger will be
age of the elder will be x + 20, and of the 3 x younger 4
4x + 80 By the conditions
+ 20 5
In 20 years
Multiplying by 5, 4x + 80
4. A man being asked the value of his horse and chaise, answered, that the chaise was worth $50 more than the horse, and that one half of the value of the horse was equal to one third of the value of the chaise. Required the value of each.
5. Two persons talking of their ages, the first says, of my age is equal to of yours ; and the difference of our ages is 10 years. What are their ages?
6. There are two towns situated at unequal distances from Boston, and on the same road. They are 30 miles apart. 3 of the distance of the second from Boston is equal to of the distance of the first. What is the distance of each from Boston ?
7. A man being asked the value of his horse and saddle, answered, that his horse was worth $114 more than his saddle, and that of the value of his horse was 7 times the value of his saddle. What was the value of each ?
8. A hare is 40 rods before a greyhound, but she can run only as fast as the greyhound. How far will each of them run before the greyhound will overtake the hare?
9. A gentleman paid 4 labourers $136 ; to the first he paid 3 times as much as to the second wanting $4; to the third one half as much as the first, and $0 more ; and to the fourth 4 times as much as to the third, and $5 more. How much did he
piy to each?
10. A man bought some cider at $4 per barrel, and some beer at $7. There were 6 barrels more of the cider than of the beer; and of the price of the beer was equal to of the price of the cider. Required the number of barrels of each.
11. Two men commenced trade together; the first put in £40 more than the second, and the stock of the first was to that of the second as 14 to 5. What was the stock of each !
14 to 5 signifies the second is ii of the first. 12. A man's age when he was married was to that of his wife as 3 to 2 ; and when they had lived together 4 years, his age was to hers as 7 to 5. What were their ages when they were married ?
13. A and B began trade with equal sums of money. In the first year A gained £40, and B lost £40 ; but in the second, A lost one third of what he then had, and B gained a sum less