9. If 16 horses consume 84 bush- 16 32 2 els of grain in 24 days, how many bushels will suffice 32 horses 48 days?

10. If the carriage of 5cwt. 3qr., 150 miles cost $24.58, what must be paid for the carriage of 7cwt. 2qr. 25lbs., 64 miles at the same rate?

24 48 2
84

336 bushels, Ans.

.19 4.75 14

11. If 7oz. 5dwt. of 33 bread be bought at 4 d., when corn is 4s. 2d. per bushel, what weight of it may be bought for 1s. 2d., when the price per bushel is 5s. 6d. ?

145

V. CANCELLING APPLIED TO THE CHAIN RULE.

The Chain Rule consists in joining many proportions together; and by the relations which the several antecedents have to their consequents, the proportion between the first antecedent and the last consequent is discovered.

This rule may often be abridged by cancelling equal quantities on both sides, and abbreviating commensurables.

NOTE. The first numbers in each part of the question are called antecedents, and the following, consequents.

1. If 20 lbs. at Boston make 23 lbs. at Antwerp, and 150 lbs. at Antwerp make 180 lbs. at Leghorn, how many pounds at Boston are equal to 144 lbs. at Leghorn?

RULE. Write the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right hand; and, if the last number stands at the left hand, multiply the numbers of the left hand column continually together for a dividend, and those at the right hand for a divisor; but, if the last number stands at the right hand, multiply the numbers at the right hand column continually together for a dividend, and those at the left for a divisor; and the quotient will be the answer.

10 12

2. If 12 lbs. at Boston make 10 lbs. at Amsterdam, and 10 lbs. at Amsterdam make 12 lbs. at Paris, how many pounds at Boston are equal to 80 lbs. at Paris?

3. If 25 lbs. at Boston are equal to 22 lbs. at Nuremburg, and 88 lbs. at Nuremburg are equal to 92 lbs. at Hamburg, and 46 lbs. at Hamburg are equal to 49 lbs. at Lyons, how many pounds are equal to 98 lbs. at Lyons?

1510
100

4. If 24 shillings in Massachu- 2 24 32 4 setts are equal to 32 shillings in 6 4845 New York; and if 48 shillings in New York are equal to 45 shillings in Pennsylvania; and if 15 shillings in Pennsylvania are equal to 10 shillings in Canada; how many shillings in Canada are equal to 100 shillings in Massachusetts ?

5. If 17 men can do as much work as 25 women, and 5 women do as much as 7 boys, how many men would it take to do the work of 75 boys?

2517
75

6. If 10 barrels of cider will pay for 5 cords of wood, and 20 cords of wood for 4 tons of hay, how many barrels of cider will it take to purchase 50 tons of hay?

1000

=831s. Ans.

12

5

7. If 100 acres in Brad-6 120 100 ford be worth 120 in Ha- 13 65 50 10

500 bls. Ans.

verhill, and 50 in Haver

hill worth 65 in Methuen,

150 25

how many acres in Bradford are equal to 150 in Methuen ?

8. If 10 lbs. of cheese are equal in value to 7 lbs. of butter, and 11 lbs. of butter to 2 bushels of corn, and 11 bushels of corn to 8 bushels of rye, and 4 bushels of rye to one cord of wood, how many pounds of cheese are equal in value to 10 cords of wood?

MISCELLANEOUS QUESTIONS.

1. Required the number of cubic feet in a box, 24 feet wide, 13 feet high, and 14 feet long?

2=2; 17 = "; 147=23.

$XX6X231 231

= =57% feet, Ans.

4× 9 × 16 4

2. What cost 15 yards of cloth, 23 yards wide, at $3 per square yard?

3. If $12 will purchase a piece of land that is 9 rods long and 6 rods wide, how long a piece that is 3 rods wido may be obtained for $94?

12=1; 91; 6=;3;= 2; 94 = 4.

4. When 18 square ròds of land are sold for $314, what is the value of 62 square rods?

181; 3 = 1; 621 = 7.

5. How many boxes that are 1 foot 7 inches high, 1 foot 5 inches wide, and 5 feet 1 inch long, will it require to hold the same quantity that a box 4 feet 9 inches wide, 2 feet 10 inches high, and 25 feet 5 inches long, would contain?

1