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which will give x=$4971.42'.

30. What amount of stock in a manufacturing establishment, at an advance of 6 per cent, could be purchased for $1200?

Let x represent the amount; then
100 100+6x1200.
This proportion will give x=$1126.76'.

Or, let a represent the amount; then since
*13

61 100, or is the ratio of percentage,

200

13x

200

We shall then have the Equation

13.x

x+

200

represents the percentage on the amount.

=1200;

which will give x=$1126.76'.

31. A quantity of damaged cloth was sold for $250, which was at a loss of 16 per cent. For what sum was the cloth purchased ?

Let x represent the sum; then

100 100-16:: x: 250. This proportion will give x=$300.

x

Or, let x represent the sum; then since

16 ÷ 100, or

50 300'

is the ratio of percentage,

50.x

represents the percentage on the cost. 300 Hence, we shall have the following Equation:

50x

300

from which we shall find x=$300.

=250;

32. The population of a city increased from 7850 to 11775 inhabitants, in one year. What was the percentum of increase during the year?

Let x represent the percentum of increase; then since the population increased 11775-7850-3925 inhabitants in one year, we shall have the proportion

100:x:: 7850 : 3925;

from which will be found equal to 50 per cent.

Or, let z represent the percentum of increase; then since

X is the ratio of percentage,

100

7850x

represents the amount of percentage on 7850.

100

Then, we shall have the Equation

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33. An agent receives $2030 to invest in merchandise-himself to retain a commission of 1 per cent on the amount of the purchase What is the sum to be invested?

Let a represent the sum; then

100 100+1:x:: 2030; from which we shall find = $2000.

=3925;

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which will give x= $2000.

34. A merchant wishes to effect an insurance on a stock of goods amounting to $3573, which shall cover both the value of the goods and the premium of insurance. What is the sum to be insured, allowing the rate to be per cent?

Let x represent the sum; then

100 100-3::x:3573;

which will give x=$3600.

3x

Or, let a represent the sum; then since

3

3

100, or

4

400

is the ratio of percentage,

"

represents the premium of insurance. 400 Then, we shall have the following Equation:

3x

400

from which we shall find x=$3600.

X

=3573;

35. What amount of stock in a Savings Bank, at an advance of 5 per cent, could be purchased for $4200? and what amount in another, at a discount of 5 per cent, could be purchased for $1995?

1st. Let x represent the amount; then 100 105 x : 4200; from which x will be found =$4000.

Or, let x represent the amount; then since

5

is the ratio of percentage,

100

5x

100

We shall then have the Equation

5x

x+

100

This Equation will give x=$4000.

represents the percentage on the stock.

=4200.

2d. Let x represent the amount; then
100 100-5: :x : 1995;

from which we shall find x=$2100.

Or, let x represent the amount; then since

5

is the ratio of percentage,

100

5x

100

We shall then have the Equation

represents the percentage on the stock.

which will give x=$2100.

100

30x

100

X

Problems in Interest, &c.

36. What principal would amount to $1000 in 5 years allowing the rate of interest to be 6 per cent ?

Let x represent the principal; then

6x

100

trx

The Equation will then be

5x

100

represents the interest for one year (174); and

represents the interest for five years.

x+

=1995;

30x

100

which will give x=$769.

37. What is the Formula for finding the principal which, at interest at r per cent, would amount to the sum a in t years?

Let x represent the principal; then

rx

x+

=1000;

represents the interest for one year; and

from which we shall find x=

represents the interest for t years.

100

We shall then have the Equation

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38. What principal would amount to $2500, in 10 years; allowing the rate of interest to be 7 per cent?

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39. At what rate per cent must $1000 be put on interest to amount to $1150 in 2 years and 6 months?

Let x represent the rate per cent; then

1000x

100

× 21, or

1000x 100 We shall then have the Equation

100

stx

100

represents the interest for one year; and

5000x

200

=2500;

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5000x

1000+

200

from which we shall find x=6 per cent.

represents the interest for 2 years,

40. What is the Formula for finding the rate per cent of interest at which the sum s would amount to the sum a in t years?

Let x represent the rate per cent; then

SX

The Equation will then be

s+

from which x will be found =

=1150;

represents the interest for one year; and

represents the interest for t years.

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