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142 Rh 4. Find a number such that six-sevenths of it shall exceed four-fifths of it by 2.

5. The fifth, fifteenth, and twenty-fifth parts of a number together make up 23: find the number.

6. Two consecutive numbers are such that one-fourth of the less exceeds one-fifth of the greater by 1: find the numbers.

7. Two numbers differ by 28, and one is eight-ninths of the other: find them.

8. There are two consecutive numbers such that one-fifth of the greater exceeds one-seventh of the less by 8: find them.

9. Find three consecutive numbers such that if they be divided by 10, 17, and 26, respectively, the sum of the quotients will be 10.

10. A and B begin to play with equal sums, and when B has lost five-elevenths of what he had to begin with, A has gained $6 more than half of what B has left: what had they at first ?

11. From a certain number 3 is taken, and the remainder is divided by 4; the quotient is then increased by 4 and divided by 5, and the result is 2: find the number.

12. In a cellar one-fifth of the wine is port and one-third claret: besides this it contains 15 dozen of sherry and 30 bottles of hock: how much port and claret does it contain ?

18. Two-fifths of A’s money is equal to B’s, and seven-ninths of B’s is equal to C’s, in all they have $770: what have they each ?

14. A, B, and C have $1285 among them: <A’s share is greater than five-sixths of B’s by $25, and C’s is four-fifteenths of B’s: find the share of each.

15. A man sold a horse for $35 and half as much as he gave for it, and gained thereby $10: what did he pay for the horse ?

16. The width of a room is two-thirds of its length. If the width had been 3 feet more, and the length 3 feet less, the room would have been square: find its dimensions.

17. What is the property of a person whose income is $430, when he has two-thirds of it invested at 4 per cent, one-fourth at 3 per cent, and the remainder at 2 per cent ?

18. I bought a certain number of apples at three for a cent, and five-sixths of that number at four for a cent: by selling them at sixteen for six cents I gain 3$1⁄2$ cents: how many apples did I buy ?

19. Find two numbers such that the one may be z times as great as the other, and their sum equal to b.