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Name _______________________________________ Date __________________ Class __________________ Practice B Solving for a Variable Answer each of the following. 1. The formula C 2r relates the radius r of a circle to its circumference C. Solve the formula for r. 2. The formula y mx b is called the slope-intercept form of a line. Solve this formula for m. ________________________________________ ________________________________________ Solve for the indicated variable. 3. 4c d for c 4. n 6m 8 for n ________________________ 5. 2p 5r q for p ________________________ 6. 10 xy z for x 7. ________________________ a c for b b ________________________ 8. ________________________ h4 k for j j ________________________ Answer each of the following. 9. The formula c 5p 215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending. a. Solve the formula c 5p 215 for p. ___________________________________ b. If Allie’s parents are willing to spend $300 for a party, how many people can attend? ___________________________________ 1 bh, 2 where b represents the length of the base and h represents the height. 10. The formula for the area of a triangle is A a. Solve the formula A 1 bh for b. 2 b. If a triangle has an area of 192 mm2, and the height measures 12 mm, what is the measure of the base? ___________________________________ ___________________________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Algebra 1 Name _______________________________________ Date __________________ Class __________________ 3.Possible answers: add 3x to each side, add 15x to each side 4. 48 5. 2 6. 5 7. no solution 8. 1 9. all real numbers 10. no solution 11. all real numbers 12. 1 SOLVING FOR A VARIABLE Practice A 1. C K 273 x 5 3. y 2. x 4 1 3. x 7 2 4. x 2 5. 2x (6) 0 or 2x 6 0 6. 9x 18 0 or 9x (18) 0 7. 5x 27 0 or 5x (27) 0 b. After writing the equation in the form ax b 0, substitute the values of a and b into the formula found in part a. 10. x 3 12. x 5 6. j 7. w v 9 8. a bc 3 9. a. t 13. x 7 14. a. infinitely many solutions 10. a. F 2 E V b. 12 Practice B y b x 1. r C 2 2. m 3. c d 4 4. n 8 6m 5. p q 5r 2 6. x 10 z y 7. b a c 8. j h4 k 9. a. p c 215 5 b. 17 1. w Problem Solving 28 feet 16 hours B C 6k h 10. a. b 2A h b. 32 mm Practice C b. no solution 1. 3. 5. 7. d r b. 3 11. x 2 2 5 4. s r 4t p 7n 3 8. 3x (21) 0 or 3x 21 0 b 9. a. x a 1 T 5. m Challenge 7 1. x 3 2. f 2. 7 days 4. 20 months 6. G Reading Strategies 1. Look for an opportunity to use the Distributive Property. 2. Combine any like terms. 3. Collect the variable terms on one side of the equal sign. 4. p 6 5. x 1 6. t 2 P 2l 2 2. vf at vi 3. f g 3 4. a 12 5b 5. x z 7y 3 6. h jk g 5 7. r s(t 9) 8. n m3 p 9. a. a F m b. 19 m/s2 10. a. t I Pr b. 8 years Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Algebra 1