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of the head in lbs., and 9++9=the weight of the head and tail, which, by the question, is equal the weight of his body;

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:. x=9++9, (an equation,)

(10.) multiplying by 2, 2x=18+x+18;
by transposition, 2x-x=18+18,
or x=36 weight of the body,

and 9+2=27, weight of the head,

9, weight of the tail,

72, weight of the fish.

Or thus:

Let 2x the weight of the body in lbs. ; then, x+9= the weight of the tail;

.. 9+x+9=2x;

by transposition, 18=x;

.. the fish weighed 36+27+9=72lbs.

3. What number is that, to the double of which if 14 be added, the sum will be 52?

Here the learner may say, if I knew the number, I could double it and add 14 to the product, and the sum would be equal to 52 by the question;

.. let the number required;

then, by the question, 2x+14=52;
by transposition, 2x=52-14-38;

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4. What number is that, from the double of which if 16 be subtracted, the remainder is 12?

Here, as above, let x = the required number; then 2x-16=12;


by transposition, 2x=12+16=28;

x= -=14.

5. Said A, I am twice as old as B; to which Canswered, I am as old as you both, and the sum of our respective ages is 90 years. What was each person's


Here, if the Student knew B's age, he would easily find the other;

.. let x B's age in years;

then, by the question, 2x A's age,

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hence, by C's answer, the sum of these three quantities is equal to 90;

.. x+2x+3x=90, or 6x=90;

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Let x


Or thus :

A's age in years; then, A being twice as

old as B, = B's age, and C being as old as A


and B together, +=C's age in years;

then, the sum of all their ages being 90 years,

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hence, A's 30, B's 15, and C's 45 years.

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6. A gentleman distributed 20s. amongst four poor people; to the second he gave twice, to the third three times, and to the fourth four times as much as the first. How much did he give to each?

Let x = the sum he gave to the first in shillings; then 2x = the sum he gave to the second;


and 4x

the sum he gave to the third;

the sum he gave to the fourth;

.. x+2x+3x+4x=20, or 10x=20;

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hence, 2s. 4s. 6s. and 8s. he gave to each respectively.

7. If the distance from Leeds to London be 192 miles, and two travellers, A and B, set out at the same time to meet each other, A from Leeds and B from London; A goes 25 miles, and B 23 miles aday. In how many days will they meet?

Let x the number of days required;

then 25x the distance A will travel before he meets B,

and 23x the distance B will travel before he meets A;

.. these distances added together will the dis tance from Leeds to London;

hence, 25x+23x=192, or 48x=192;

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8. A Wine Merchant sold 12 gallons of wine, at a certain price per gallon, and afterwards 17 gallons more at the same rate, and received £4. 5s. more at this sale than at that. Required the price per gallon. Let the price per gallon in shillings;

then 12x the sum received for 12 gallons,

and 17

the sum received for 17 gallons;

.. by the question, the difference of these sums is = £4. 5s. or 85 shillings;

hence 17x-12x=85, or 5x=85;

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9. Divide a sum of money amongst A, B, C, and D, as follows: give to B 5s. more than to A, and to C 2s. more than to B, and to D 6s. less than to C; the sum to be divided is 1s. more than 8 times the sum given to A. Required each person's share.

Here, if the Student knew the sum given to A, he would readily determine the rest ;

.. let x A's share in shillings;


then x+5= B's share in shillings;


and +1

C's share in shillings;

D's share in shillings;

now, the sum to be divided being one shilling more than eight times A's share;

.. 8x+1= the sum to be divided, which, by the question, will be equal to the sum of their shares

· x+x+5+x+7+x+1=8x+1,

or 4x+13=8x+1;

by transposition, 8x-4x=13—1,
or 4x=12; .. x=3;

whence, A's 3, B's 8, C's 10, and D's 4 shillings.


10. A and B, with each an equal number of marbles, began to play with C and D; after a certain number of games, A found that he had won 10, and that B had lost 20; A had now twice as many as B. How many had each at first?

Let x the number each had at first;

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then x+10= the number A had after playing, and a 20 the number B had after playing; .. by the question, A's number being equal to twice B's, 2.(x-20)=x+10, or 2x-40=x+10;

by transposition, 2x-x=10+40; x=50.

11. A farmer has two stacks of hay, each containing the same number of tons; from one of them he sells 7 tons, and from the other 14, and then found that twice as much remained in one as the other. Required the number of tons in each stack at first.

Let x the number of tons in each;

then x-7= the tons left in one,

-14 the tons left in the other;

and x

.. by the question, 2(x-14)=x-7,
or 2x-28-x-7;

by transposition, 2x-x-28-7; .. x=21.

12. A farmer bought 12 sheep for £10. 12s.; for part of which he gave 23s. a head, and for the rest 15s. a head. Required the number of each.

Let x the number at 23s. a head;
then 23a their price in shillings;
also, 12-x= the number at 15s. a head,
and 15.(12-x), or 180-15x = their price;
.. 23x+180-15x=212;

by transposition, 23x-15x=212-180,

or 8x=32;..,x=4;,.

whence, there were 4 at 23s: and 8 at 15s. a head.

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