QUEST. CCII. Two mafons A and B jointly perform a piece of work in 12 days; now if the fum of the days in which they could each have feparately performed the fame, be multiplied by the days in which A alone (he working quicker than B) could have done it, the product will be 1000 In what time could each do it?

Suppofe A could do it alone in x days,

y days;

12

Then (1:12:)

the work done by A,

x

in 12

I 2

And († : 1 :: 12 ; ) — the work done by B,

days;

X-12

But (x+xx) xx+xy=1000 by quest.

If x=-1

Or x3 — 12xx+12x2=1000x-1200;

Th. x3-1000x+12000=0.

12999=0:1,3,7,21,619,

are div.

QUEST. CCIII. 4. B, and C, who among them had 2000 fhillings, went to play, and B loft to A the fquare root of what A began with, and had 341 fhillings left; but if he had loft to C the cube root of what C began with, he would have had 362 fhillings left: What fum had each at first?

Suppofe A had x; B, y; and G, ≈ shillings;
Then x+y+=2000; ory=2000

Whence

Or

Th.

Now (by ift and 3d

} 362 +:

I

341+x= 362 + z

I

x2= 21+23;
x = 441 + 42 x 3 3 + x 3

=2000-441-422

x + x +43 x 3 — 1197=0.

Then

by queft.

1099=0:1 14,7,157,

Where 11, 10, 9, 8, 7, differ by unity;

And 2+23+4323—1197—x3+10x3+133;

are divifors;

Suppose to x men and y women,

him 64 fhillings: How many men and women did he fquare of the number of poor women, it would have cost given a like fum to a number of perfons equal to the as many pence as there were poor men; now if he had among fome poor perfons, men and women, and to each QUEST. CCIV. A charitable perfon gave 20 fhillings

give to?

Then (x+yxx=) xx+xy=(2012) 240 by quest.

And

yyx=(64×12=)

768

240—xx=(xy=) ;

768 240- =(xx=

y

768 589824

240

=

5

768 S

y

768

which divides by 12X4:

Th. 54-163-12288=0. If y=-1; Then 12267=0:1 y= 0; Then 12288=0:

y=

1; Then 12299=0;!,7,49,251,

Where 9, 8, 7. differ by (unity) a divifor of (5) the coeficient of (*) the highest power of (y) the unknown quantity;

QUEST. CCV. If the product of the folidities of two cubes, whofe fides differ by 4, be multiplied by the folidity of the greater, it will produce 3176523: What are their fides?

6

Or y+4 xy3=(3176523=) 1475

-2

Th. y+4xy (147) 49 × 3,

I

And y+4x=73; Th. y+4y=7√3
Subftitute x-x for; and x3-x3 for 7/3:
Then x3-3x*x+3x2-x3+4x-4x=x3-x3,
Th. 4×2-x=3xxxx-x; And ‡x=x:

2

QUEST. CCVI. What two numbers are thofe, whofe fum, and product, being feverally multiplied by the leffer will produce 175, and 250?

If = the greater, and y= the leffer of those numbers;

Then (x+yxy=) xy+y=27,5} per queft.

And

(xyxy=)

175-yy

y

250 =(x=) ;

1751-3=270: here y E1, and 2. y=1,4458, &c. See the operation below*,

Or

8

2

2000=2073-1346r—36r2+or

3

(By tranfp) 1346r+36r2—8, 3 =73:

3d

(1323,05=) 0,054156=r:

1346r+36r, r−7 r r r = 73,

That is 1346r+1,949616r-0,023456r=73;
Th. r=3479267&=0,0541572, &c.

Now
That is 1,5-0,05415721,4458429, &c. =y.

* This operation is conformable to Dr. Halley's rationaltheorem.