Prob. 9. The Sum of two Numbers 14, and the differ ence of their Squares 56, required the Numbers? Prob. 10. The product of two Numbers being 45, and their Quotient 1, 8 required the Numbers? Prob. 11. What two Numbers are thofe whofe Sum is 40, and Product only 4, with a Theorem for all fuch Questions? Let 40=2a, 4b,x= Diff. of the Numbers. then a+x greater and a-x lefs Number. a2x2-b a2-b x2 x=/a2b=19,899 2-x=0,101 Prob. 12. Required two Numbers whose Product is 12, and the difference of their Squares 7 ? Prob. 13. A Gentleman being asked how many Guineas he had in his pocket? answered, if the Number I have be multiplied by 4, and the Square Root of the Product be added to the Number of Guineas I have in my pocket, that Sum will be equal 440, required the Number? Prob. 14. What number is that which being divided into 4 or 5 equal parts, the Product of all the parts in both Cafes fhall be exactly the fame. x=the Number. X X X X X X X X X -X-X-X--X-×-X-X-P.Q 256 256 Prob. 15. A Merchant fhips Goods for Jamaica, to the Amount of 500; pays for Infurance 5 per Cent. for prompt Payment 3 per Cent. how much money ought the Merchant to infure, fuppofing the Goods to be loft, that he fhall be no lofer? Prob. 16. You that are skill'd in mathematic Arts, Divide 100 into two such Parts, That when those Parts each other hath divided, Their Quotients make just 5, if right decided?. Gives. x= Diff. of the Numbers, 100—2a; b=5 +greater and a-x-less Number. -+ a-x a-xa+x=b P. 2. which reduced b+2=32,7326 hence 82, 7326 and 17, 2674 are the Parts. Prob. 17. x Shews the Years, and y the Months explain, Hence by a Quadratic. you my age May gain. 2 } } x2y + xy2=8580-a 2 x2y3+x3у21335480b b 213 xy=156=n Reqdx and y |