A Treatise of Algebra. 81

ef what he had to receive : Therefore we have thisEquation 28x—320 = 380; whence 28* (=3804.320) =700, and * = = 25, equal to the Number

of Days he work’d j therefore 40 — x, theNumberofDays he play’d, will be = 1 J : Which is proved thus, 25X 20— 15x8 = 500- 120=380.

PROBLEM VIII.

A Farmer would mix twt Sorts of Grain, viz. IVheat,worth 4 Shillings a Bujhcl, with Rye, worth 2$. 6 d. aBushel, so that the whole Mixture may constji of 100Bushels, and be worth 3 s. and zd. aBuJhel: Now’tisrequired to find how many Bushels of each Sort must betaken to make up such a Mixture.

Let the Number of Bushels of Wheat be put = a,and the Number of Bufhelsof Rye will be ioo»— x: Butthe Number of Bushels multiply’d by the Nuihber ofPence per Bushel is equal to the Number of Pence theWhole is worth ; therefore 48*, is the whole Value of theWheat, and 30 x 100 — a- or 3000 — 30A that of theRye, and consequently, 4.8* 4-3000 — 30A, the Sum ofthese two, the whole Value of the Mixture ; which, bythe Question, is equal to 100 x 38, or 3S00 Pence:Hence we have 48A -f- 3000— 30A = 3800, that is,i8 a -f* 3000 = 3800, or 1 8a = 800, and confe*-quently x = Ns = 444, the Number of Bushels ofWheat; whence the Number of Bushels of Rye will be100 — 441 = 555.

PROBLEM IX.

The Difference os two Numbers being given, equal to 4,and the Difference of their Squares , equal to 40 ; to findthe Numbers. -

Let the lesier Number be a 3 then, the Difference be-st^ 4 > greater must consequently be a -)- 4» and it’sSquare a a 8x -f- 16, from which, aa, the Square ofthe lesier being taken, the Difference is 8 a- j- > 6: There-fore 8a -f- 16 = 40 ; which, reduced, gives a = 3 ;

G whence