I

2. What number is that, whose part exceeds its

Whence x=192 the number required.

3. Divide 1000l. between A, B and C, so that A shall

have 721. more than B, and C 100l. more than A.

Let x=B's share of the given sum,

Then will x+72=A's share,
And x+172 =C's share,

And the sum of all their shares x+x+72+x+172,

Or 3x+244 1000 by the question;

That is, 3%=1000-244-756,

4. A prize of 1000l. is to be divided between two persons, whose shares therein are in the proportion of 7 to 9; required the share of each.

Let x equal first person's share,
Then will 1000-x equal second person's share,
And x: 1000-x:: 7: 9, by the question,

That

That is, 9x=1000-x×7=7000-70
Or 16x7000,

7000

Whence = 허=4371. Ios. = first share,

And 1000-x=1000-4371. 10s. = 5621. IOS. 2d share.

5. The paving of a square at 2s. a yard cost as much as the inclosing of it at 5s. a yard; required the side of the square.

Let x equal side of the square sought,

Then 4x yards of inclosure,

And yards of pavement;

Whence 4X5=20x equal price of inclosing,.

2

And x2=2x equal price of paving.

But 2x2 = 20x by the question,

2

Therefore, **=10%, and x=10=length of the side

required.

6. A labourer engaged to serve for 40 days upon these conditions, that for every day he worked he should receive 20d. but for every day he played, or was absent, he was to forfeit &d.; now at the end of the time he had to receive 11. 115. 8d. The question is to find how many days he worked, and how many he was idle.

Let x be the number of days he worked,

Then will 40-x be the number of days he was idle; Also X20 20x = sum earned,

And 40-xX8=320-8x=sum forfeited,

Whence 20x-320-8x380d. (11. 115. 8d.) by the

question, that is, 20x-320+8x=380,

Or 28x380-320 = 700,

Andx=25= number of days he worked,

And 40-x=40-25=15= number of days he was 7. Out of a cask of wine, which had leaked away, 21 gallons were drawn; and then, being gauged, it appeared to be half full: how much did it hold ?

Let it be supposed to have held x gallons,

X

And consequently there had been taken away 21-+-gal,

Or x = 126 = number of gallons required.

3

8. What fraction is that, to the numerator of which if I be added, the value will be; but if I be added to the denominator, its value will be ?

Hence 4x-3x-3=1+1-y,

That is, x-3=1,

I

Or x=4, and y=3x+3=12+3=15;
fraction required.

So that

9. A market woman bought a certain number of eggs, at 2 a penny, and as many at three a penny, and sold them all again at the rate of 5 for 2d. and, by so doing, lost 4d. What number of eggs had she ?

Let

Let x = number of eggs of each sort.

Then will

And price of the second sort.
3

But 5: 2:: 2x (the whole number of eggs) :

4x 3 5

price of both sorts together, at 5 for 2d.

Whence x=120= number of eggs of each sort required.

10. A can do a piece of work alone in ten days, and B in thirteen; if both be set about it together, in what time will it be finished ?

Let the time sought be denoted by x,
Then 10 days: I work :: x days :

And 13 days: I work :: * days :

20

X

X

13

Hence - = part done by A in x days;

10

And

13

= part done by B in x days.

10

10

13

That

And therefore 23x=130, or x==5days, the time required.

11. If one agent A alone can produce an effect e in the time a, and another agent B alone in the time b; in what time will they both together produce the same effect ?

Let the time sought be denoted by x.

ex

Then a: e::x: -= part of the effect produced by A,

And b:e::x:

Whence

Or

a

a

That is, *+

ex

b

ax

Ι;

=a; b

1. What two numbers are those, whose difference is 7, and sum 33 ? Ans. 13 and 20.

2. To divide the number 75 into two such parts, that three times the greater may exceed seven times the less by

15.

Ans. 54 and 21.

3. In a mixture of wine and cider, of the whole plus 25 gallons was wine, part minus 5 gallons was cider;

how many gallons were there of each?

Ans. 85 of wine and 35 of cider.

A