15. With the multiplier 48, the product is 166656; with a multiplicand 1 third as great, what would be the product? 16. The divisor is 16, the quotient 12624; with a divisor 1 fourth as great, what would be the quotient? 17. The divisor is 24, and the quotient is 43950; if the divisor be made 6 times as large, what will be the quotient? 18. The quotient is 91864; with a divisor 1 ninth as great, what would be the quotient? 19. A grocer bought two kinds of syrup; one for 54 cents a gallon, and the other for 62 cents. What was the average cost a gallon? OPERATION. (54 cents+62 cents)÷2-58 cents. The average of two numbers is one-half their sum, the average of three numbers is one-third their sum, etc. 20. A merchant bought equal quantities of 3 kinds of tea, some at 60 cents, some at 78 cents, and some at 90 cents a pound. What was the average cost a pound? 21. A keeper of a toll bridge received $104 toll on Monday, $97 on Tuesday, $128 on Wednesday, and $99 on Thursday. What were the average daily receipts? 22. Sold 3 city lots for $1500, $2976, and $1895, respectively. What was the average price? 23. If a young man receive a salary of $25 a week, and he pays $8.75 for his board, and $4.65 for other expenses, in how many weeks can he pay a debt of $487.20? 24. A man having $4578 paid out all but $1642 in 8 weeks. What was the average amount paid out each week? 25. Bought 140 acres of land for $7560, and sold 86 acres of it at $75 an acre, and the remainder at cost. How much was gained? 26. A father gave his property to his 4 children. To the first he gave $6780, to the second $8200, to the third $1526 more than to the first, and to the fourth $1345 less than to the third. What was the value of his property? 27. The sum of two numbers is 184, and their difference is 42. What are the numbers? ANALYSIS.-Since 184 is the sum of the numbers, if the differ ence 42 be subtracted from the sum 184, the remainder 142 will be twice the less number. 142 ÷ 2 = 71 the less number; and 71+48 113 the greater number. = Or, if the difference 42 be added to the sum 184, the amount 226, will be twice the greater number. 226 ÷ 2 =113 the greater number; and 113-4271 the less number. PROOF.-113 + 71 184 the sum. = 28. The sum of two numbers is 5672, and their difference is 1974. What are the numbers ? 29. A man paid $1250 for a horse and carriage, the horse being valued at $190 more than the carriage. What was the value of each? 30. At a town election the whole number of votes cast for two candidates was 3789, and the majority for the successful candidate was 227. How many votes did each receive? 31. Two men are worth $28475, and one is worth $4625 more than the other. How much is each man worth? 32. A grocer wishes to put 240 pounds of tea into three kinds of boxes, containing respectively 5, 10, and 15 pounds, using the same number of boxes of each kind. How many boxes will be required? 33. Sold a quantity of wood for $2492, that cost $1424, thus gaining $3 a cord. How many cords were there, and what was the cost per cord? 34. What number divided by 36, the quotient increased by 48, the sum diminished by 37, the remainder multiplied by 14, and the product increased by 216÷72, is 269? Find the missing term in the following equations: 35. (15341÷29) × (8430÷1405)=1587×? 36. [4500+(12000—1375)÷121 × 25] × 48=? ×24 37. 732 × 6-÷(15 x 24÷9 × 10)+(42 × 234÷26)=? 38. 450+(24—12) × 5÷(90÷6)+(3 × 11—18=? 146. The pupil should illustrate the following problems by original examples: PROBLEM 1. Given several numbers, to find their sum. 2. Given the sum of several numbers and all of them but one, to find that one. 3. Given the parts, to find the whole. 4. Given the whole and all the parts but one, to find that one. 5. Given two numbers, to find their difference. 6. Given the greater of two numbers and their difference, to find the less. 7. Given the less of two numbers and their difference, to find the greater. 8. Given the minuend and subtrahend, to find the remainder. 9. Given the minuend and remainder, to find the subtrahend. 10. Given the subtrahend and remainder, to find the minuend. 11. Given two or more numbers, to find their product. 12. Given the product and one of two factors, to find the other factor. 13. Given the multiplicand and multiplier, to find the product. 14. Given the product and multiplicand, to find the multiplier. 15. Given the product and multiplier, to find the multiplicand. 16. Given two numbers, to find their quotient. 17. Given the divisor and dividend, to find the quotient. 18. Given the divisor and quotient, to find the dividend. 19. Given the dividend and quotient, to find the divisor. 20. Given the divisor, quotient, and remainder, to find the dividend. 21. Given the dividend, quotient, and remainder, to find the divisor. 22. Given the final quotient of a continued division and the several divisors, to find the dividend. 23. Given the quotient of a continued division, the first dividend, and all the divisors but one, to find that divisor. 24. Given the dividend and several divisors of a continued division, to find the quotient. 25. Given two or more sets of numbers, to find the difference of their sums. 26. Given two or more sets of factors, to find the sum of their products. 27. Given two or more sets of factors, to find the dif ference of their products. 28. Given the sum and the difference of two numbers, to find the numbers. |