CALIFORNIA JUNIOR HIGH SCHOOL MATHEMATICS SECOND BOOK CHAPTER I REPRESENTING NUMBERS BY LETTERS. 1. The use of letters as numbers. In the First Book it has been shown that the use of letters to represent numbers gives a kind of shorthand in which rules may be written and remembered, and that many problems can be solved by substituting for the letters the numbers which they represent. But these formulas may be used in other ways to solve much more difficult problems and to discover new rules. In order so to use them, however, it is necessary to acquire some skill in handling letters representing numbers. The pupil must learn to use these new symbols in adding, subtracting, multiplying, and dividing numbers; he must also learn how to interpret a problem expressed in these symbols. 2. The use of letters to shorten statements. The pupil has learned that The sum of two numbers x and y is written x+y. The quotient of x divided by y, is written or x÷y. x y The pupil must acquire skill in interpreting these forms and in using them with both letters and figures. Exercise 1 1. A boy has m marbles and finds 10 more. has he then? How many 2. In an orchard of n trees 17 trees die. How many trees are then alive? 3. In a class there are x boys and y girls. How many pupils are there in the class? How many more boys than girls? 4. What is the perimeter of a triangle if the sides are a, a, and b? If the sides are a, a, and a? If the sides are 2x, 3k, and 16? 5. What number is 35 more than x? What number is 67 less than 2y? 6. What is the cost of y yards of cloth at n cents a yard? 7. How many dollars in c cents? 8. It costs d dollars a hundred to get some bills printed. How much does each bill cost? 9. What is the next integer after 8? After 14? What must be done to an integer to get the next integer following it? 10. If a is an integer, what is the next integer after it? What is the next integer before it? 11. How far does a train go in t hours at the average rate of m miles an hour? 12. If a man walks x miles in 5 hours what is his rate per hour? If he walks y miles in h hours what is his rate per hour? 13. What number is 8 greater than 3 times x? 14. A has x dollars, B has twice as much, and C has $36 more than B. How much has B? How much has C? 15. How many inches in ƒ ft.? In f ft. 6 in.? 16. What number is of n more than n? 17. What number is & of m less than m? 18. What number is 3 times h more than k? 19. The numbers 1, 2, 3, 4, 5 are consecutive integers. Name four consecutive integers beginning with 8. What must be added to an integer to get the next consecutive integer? Suppose that n is an integer. Name the next four consecutive integers. 20. A man who is 11 miles from home walks toward home at the rate of 3 miles an hour. How far from home is he at the end of 3 hours? 21. A and B are traveling in automobiles in the same direction. A is 15 miles behind B, and is traveling 6 miles an hour faster than B. How long before A will overtake B? 22. A man who is m miles from home walks toward home at the rate of 3 miles an hour. How far from home is he at the end of t hours? How far from home would he have been if he had walked away from home instead of toward it? 23. In exercise 21 suppose that A is k miles behind B and travels r miles an hour faster. How long before A will overtake B? 24. While the hour hand passes over 5 minute spaces how far does the minute hand go? The minute hand goes how many times as fast as the hour hand? 25. While the hour hand passes over h minute spaces how far does the minute hand go? 26. A boy is now m years old. How old was he 4 years ago? 27. A man is y years old. How old will he be in r years? 28. What is the cost of y yards, ƒ feet, 6 inches of ribbon at 3 cents a foot? 29. A string is just long enough to wind 6 times around a wheel whose radius is r inches and have i inches over. How long is the string? 30. How much longer is the circumference of a circle of radius r than one of radius 2? |