capable of Innumerable Answers.

3*9

The Proof of the firjl Answer.

Gallons of Wine at 24 pence per Gallon , together with 27 Gallons at 22 pencet(, e j on > and 3 x Gallons at j 8 pence per Gallon, amount to 1200 pence ; which is ajsoa Ue of 60 Gallons at 20 pence per Gallon.

gVEST. 20.

8 ^' ntf| er having four forts of Wines, whose prices per Quart are 1 6 pence, 10 pence,s/ nce 3 .and 6 pence, desires to make a Mixture out of them that may contain 100 Quarts,6 p S mixt Quantity being fold at some mean price per Quart between 1 6 pence andtop po fe at 12 pence, may produce the fame fumm of money, as all the particulart 0 c t ' tles or Wine in the Mixture if they werefold at their own prices. The Question is*a ^hat quantity of Wine of each sort may be taken to make that Mixture ?th e M-*’ e> J an( i 11 P ut ^or the unknown Quantities of Wine that are sought to make1 lxt ure . then a -J -7 -|- u = 100, (the total number of Quarts in the Mixture,)

P t0 , V multiplying those Quantities severally into their peculiar prices, the fumm of the^lt'r IS - l6a ~\~ roe-j- which fumm must be equal to the Product of iop

'Plied into 12, that is, 1200 pence ; So that the Question may be stated thus;

I. ]f

s, a* » . . . 100

^"d .. i 6 a-\+ice-\~%]-\-‘ 6 u = 1200

^hat are the numbers a, e t y and « ? | j »> ■ ■■—•—— .

thg given Equations being fewer in multitude than the numbers sought, it’s a sign thatof Question is capable of innumerable Answers; now that you may find out as manyjJ hc, n as you please, the first scope in the Resolution must be to discover limits to directfcq !, 1 ?h°ice of some one of the numbers sought, and accordingly, the drift in the eight*^ions next following is to search out limits for the first number a.

3( RESOLVTIO N.

the first Equation by transposition of 4, this£ _ I00 -*

3 n d from the second Equation by transpositions . 1 01 s _

J. 1 ^ 4 ,thisariseth, ....... .5 = 1100-16*

1 J’e third Equation multiplied by 6 , to wit, theT

. of the known numbers which are prefixt to the( ^ , ,■

in the first part of the fourth Equation , pro-£ = 6qo-6m

t j^gain, the third Equation multiplied by 1 o, that is, T

e greatest of the known numbers which are prefixtC T/ . „ , ___

letters in the first part of the fourth Equations ^ °-H"* IC —

isVr tIlan '^ that the first part of the fifth Equations

l ^larrl han thefi / st ,. pa ir u°n h n[° U , r£ ?’ ^°> 6oO~6a^ I 200 -I *4

&av ter part of the fifth shall be less than the latter^

8 . -p? °f the fourth, viz . 3

/i: ere fore from the seventh step, after due Redu- ? _

S.T n 3 it follows, that ..5 60

£qi ' Por as much as the first part of the sixth*}

th leS h ,FTV hanlhe fir ? P f °r i e l° n r ^> 1000- ic* c“ 1200- 1*4Ste CI ° re a Po r ^ e * atter P arC ^ a be(

-p^ er than the latter part of the fourth, viz. . .J

duct.- *° re from the ninth step, after due Re-? . , , 3 i

^tion , it follows that .s 4 ^ 333

Us ^ ce it is found by the eighth and tenth steps, that a the number of Quarts sought" ^ ort of Wine to make the Mixture must be less than 60, but greater than 33*,e nu mber within those limits be taken for the value of a , viz.

it. Suppose