Exercise 11 1. Write a formula for finding the sum, s, of two numbers a and b. 2. Write a formula for finding the weight, w, of a barrel of crackers, if the weight of the barrel is b and the weight of the crackers is c. 3. Make a formula for finding the number of gallons of water, g, that run through a pipe in 25 minutes at the rate of n gallons a minute. 4. Make a formula for finding the number of cents, C, in d dollars and 4 dimes; for finding the number of cents, C, in d dollars, n dimes, and 3 cents. 5. Find the average of the two numbers 7 and 9. How is the average of any two numbers found? 6. Make a formula for finding the average, A, of any two numbers x and n. 7. Make a formula for finding the combined weight of a hen and 9 chickens, if the weight of the hen is h pounds and the weight of each chicken is c pounds. Represent the combined weight by W. 8. A boy walks 3 mi. each hour for 2 hours. How far does he walk in the two hours? 9. How far does a train run in 7 hours if it runs 25 miles each hour? 10. A boy runs 8 yd. each second for 12 seconds. What distance does he run in that time? The distance an object moves in one unit of time is called its rate of motion. 11. A river flows at the rate of 2 mi. an hour. How far will an object floating in it move in 8 hr. 20 min.? 12. How long will it take a man to drive 20 mi. at the rate of 8 mi. an hour? 13. How long will it take a train to run 640 mi. at the rate of 32 mi. an hour? 14. How can you find the distance an object moves in a given time at a given rate? 15. Make a formula for finding the distance, d, which an object moves at the rate, r, in the time, t. 16. Find the rate of a bicyclist who rides 32 mi. in 4 hr. 17. Find the rate of a train which runs 414 mi. in 9 hr. ; of a train which runs m mi. in 9 hr. ; of a train which runs m mi. in h hr. 18. Calling the rate r, the whole distance d, and the time t, state the formula for finding the rate when the time and the distance are known. 19. Calling the weight of a basket b, the weight of an egg e, and the weight of an apple a, make a formula for finding the total weight, W, of a basket containing a dozen eggs and 25 apples. It is sometimes convenient to use A formula to stand for different numbers. major" and a is read "a minor." and a in the same A is then read "A 20. Make a formula for finding one factor, F, of a product, when the product, p, and the other factor, f, are known. 21. Make a formula for finding the dividend, D, when the divisor, d, and the quotient, q, are given. 22. Make a formula for finding the dividend, D, when the divisor, d, the quotient, q, and the remainder, r, are given. 23. How can the divisor be found when the dividend, quotient, and remainder are known? State this rule as a formula. 24. State the formula for finding the area, A, of a rectangle whose length is 7 and width w. 13. Formulas for practice. These formulas which you have had should be remembered. Formula 1 is the cost formula. Formula 2 is the rule for the area of a rectangle whose length and width are given. Formula 3 is the formula for the distance passed over by a body moving at the rate r for the time t. Formula 4 is the rule for the volume of a rectangular solid. Other formulas which you have made but which need not be remembered are: (a) D=dq. Formula to find the dividend when divisor and quotient are given. (b) D=dq+r. To find the dividend when there is a remainder. (c) T=12e+25 a+b. To find the total weight, T, of a basket with 12 eggs and 25 apples. (d) F=p÷f. To find one factor of a given product when the other factor is given. (e) A: = x + n 'To find the average of two given numbers. If given the values of the letters supposed to be known in these formulas, these values may be substituted for the letters and the value of the letter on the left may be found by performing the indicated operations. EXAMPLE. Using formula c, find the total weight of a basket containing a dozen eggs weighing 2 ounces each and 25 apples weighing 3 ounces each, the basket weighing 14 ounces. SOLUTION. We know that e=2, a=3, and b = 14. W=12X2+25×3+14=24+75+14=113. Exercise 12 1. Find D of formula (a), if d=15 and q=6. 2. Find C of formula 1, if n = 20 and p=37. 3. Find F of formula (d), if p=108 and ƒ=6. 4. Find T of formula (c), if e=1.9, a= 2.1, and b=10. 5. Find D of formula (b), if d=14, q=8, and r=9. 6. Find A of formula 2, if l=12 and w=3}. 7. Find d of formula 3, if r=} and t=6. 8. Find T of formula (c), if e=2.1, a=2, and b=3. 9. Find D of formula (b), if d=247, q=43, and r=203. 10. Find A of formula (e), if x=974 and n=863. 11. Find T of formula (c), if e=2, a=3.6, and b = 12.8. 12. Find F of formula (d), if p=603 and f=7. 13. Find V of formula 4, if l=5.8, w=.3, and h=25. 14. Find d of formula 3, if r = 12.7 and t=65. Use the formulas to find the results in the following: 15. If a certain number is divided by 67, the quotient is 19 and the remainder 46. Find the number. 16. Find the volume of a piece of steel 6 in. long, .3 in. wide, and .2 in. thick. 17. How far does sound travel in 1 minute if it travels 1080 ft. in one second? 18. The product of two numbers is 9.864 and one of the numbers is 12. Find the other number. 19. The product of two numbers is 15 and one of the numbers is 105. Find the other number. 20. Find the average of 21 and 31. 21. Find the average of 17 and 373. 22. What is the average of two numbers a and b? REVIEW OF FRACTIONS 14. Reduction of fractions. 5. How can you find what part one number is of another? EXAMPLE. 18 is what part of 54? SOLUTION. 18 is 1 of 54. may be reduced to its lowest terms by dividing both numerator and denominator by 18. Therefore 18 is of 54. A fraction is reduced to its lowest terms by dividing both numerator and denominator by their greatest common factor. Exercise 13 Practice until you can read these twenty-five fractions in their lowest terms in 90 seconds. 25. In a certain schoolroom there are 12 boys and 18 girls. What part of the pupils in the room are boys? What part are girls? 26. A basketball player tries 27 throws at the basket and misses 12 times. What part of his throws are successful? 27. A ball team wins 14 games and loses 6 the first month. The second month it wins 15 games and loses 9. What part of the games played did it win the first month? The second month? |