<aADRATIC EC^ATIONS. 369 



5. A grazier bought as many sheep as cost him 60L 

 and after reserving 15 out of the number, he sold the re- 

 mainder for 54I. and gained 2s. a head by them ; hovw ma- 

 ny sheep did he buy ? Ans. 75. 



6. There are two numbers, whose difference is 15, and 

 half their product is equal to the cube of the less number; 

 what are those numbers ? Ans. 3 and 18. 



7. A person bought cloth for 33I. 15s. which he sold 

 again at 2I. 8s. per piece, and gained by the bargain as 

 much as one piece cost him ; required the number of 

 pieces. Ans. 15, 



8. What number is that, which b^ing divided by the. 

 product of its two digits, the quotient is 3 j and if 18 be 

 added to it, the digits will be inverted ? Ans. 24. 



p. Whaf two numbers are those, whose sum multiplied 

 by the greater is equal to 77 5 and whose difFcrence mul- 

 tiplied by the less is equal to 1 2 ? Ans. 4 and 7. 



I o. When will the hour, minute and second hands of a 

 clock be all together next after 1 2 o'clock ? 



Ans. Only at 12 o'clock. 



xr. The sum of two numbers is 8, and the sum of 



their cubes is 152 ; what are the numbers ? 



Ans. 3 and 5* 



12. The sum of two numbers is 7, and the sum of their 

 fourth powers is 641 ; what are the numbers ? 



Ans. 2 and 5.. 



13. The sum of two numbers is 6, and the sum of 

 their fifth powers is 1056 ; what are the numbers i 



Ans. 2 and 4. 



14. The sum of four numbers in arithmetical proj^res- 

 sion is 56, and the sum of their squares is 864 ; what are 

 tjie numbers ? Ans. ^, 12, 16 and 20. 



Y Y 



