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 Or, let a represent the amount; then since 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 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; 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 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 38. What principal would amount to $2500, in 10 years; allowing the rate of interest to be 7 per cent? 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; 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. |