Chapters 1 and 2 Cumulative Review Exercises 191 c. 4.5x - 3.6 + 2.9x = 8.2x - 5.04 d. 10(3 - x) - 5x = 20 + 5(2 - 3x) e. 4z + 32 - z = 5 - 6z f. - 2 3 (6x + 12) + 10 = x + 5 g. -0.8y + 18.4 = 3.7y + 5.8 h. 4(3x - 1) = 4(x - 1) + 8x For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. (Section 2.2, Objective 4; Section 2.3, Objectives 3 and 4 ) 34. Twice the sum of a number and 6 is the same as three times the number. Find the number. 35. The cost to rent a midsize car for one day is $58 plus $0.35 per mile. The daily cost is represented by the expression 58 + 0.35x, where x is the number of miles driven. How many miles has the car been driven if the cost of the rental car is $250.50? 36. The sum of three consecutive even integers is 102. Find the integers. 37. The sum of the two smaller of three consecutive even integers is the same as 40 less than three times the largest integer. Find the integers. 38. Solve each equation. If the equation is a contradiction, write the solution as ∅. If the equation is an identity, write the solution as . (Section 2.4, Objectives 1– 4 ) a. 3(2y + 3) - 2(y + 2) = 4(y + 1) + 1 b. 3 5 x - 4 = 7 10 x c. 0.6x + 1.8x = 960 d. 0.021x + 0.012(840 - x) = 15.12 e. 5 6 (x - 2) = 1 6 (5x - 8) + 1 3 39. The formula A = P(1 + r)t calculates the amount of money in an account at the end of t years if P dollars invested at an annual interest rate, r. (Section 2.5, Objective 1 ) a. Find the value of A if $4800 is invested for 2 yr at 1.5% annual interest. b. Find the value of P if $5181.62 is expected to be accumulated at the end of 2 yr at 1.8% annual interest. 40. The distance d, rate r, and time t of an object in motion can be related by the formula d = rt. (Section 2.5, Objective 1 ) a. Find d if r = 65 mph and t = 3.2 hr. b. Find t if d = 203 mi and r = 58 mph. 41. The revenue R, unit price p, and sale level x of a product are related by the formula R = xp. (Section 2.5, Objective 1 ) a. Find R if p = $112.50 and x = 60. b. Find p if R = $2249.10 and x = 90. 42. Use the perimeter, area, or circumference formula to find the indicated quantity. (Section 2.5, Objective 2 ) a. Find the perimeter of a rectangle if its area is 400 in.2 and its length is 16 in. b. Find the area of a rectangle if its perimeter is 92 m and its width is 18 m. 43. Solve each formula for the specified variable. (Section 2.5, Objective 3 ) a. A = lw for l b. C = 5l + 6w for w c. 3x - 8y = 24 for y d. 0.02x + 0.05y = 4.5 for x 44. Find the measure of each unknown angle. (Section 2.5, Objective 5 ) a. Find the measure of an angle whose complement is 20º less than the measure of the angle. b. Find the measure of an angle whose supplement is 64º more than the measure of the angle. c. The supplement of an angle is 42º more than three times its complement. Find the measure of the angle. 45. Find the measure of each angle labeled in the figure. (Section 2.5, Objectives 4 and 5 ) a. a 5 ° 4a – 35 ° b. 9x – 12 ° 3x 60 ° c. a° 5a 8 ° 2a 4 ° 46. In triangle ABC, the measure of angle B is 18° less than the measure of angle A. The measure of angle C is 45° more than the measure of angle A. Find the measure of each angle in the triangle. (Section 2.5, Objective 5 ) Solve each problem. Write an appropriate equation, solve the equation, and write the answer in complete sentences. (Section 2.6, Objectives 1–5 ) 47. A 46-in. LED-LCD HDTV is on sale for $975. This is 35% off the original price. What is the original selling price of the TV? 48. A sweater is on sale for $31.50. If this price is 65% off the original price, what is the original price of the sweater? 49. Kye invested $2500 in two accounts. He invested $1500 in a mutual fund that pays 2.4% annual interest and the remaining amount in a money market fund that pays 1.6% annual interest. How much interest did he earn from the two accounts in 1 yr? 50. Richard needs to make 72 L of a 25% hydrochloric acid solution. How much 40% hydrochloric acid solution and how much 10% hydrochloric acid solution should be mixed to get 72 L of a 25% hydrochloric acid solution?
hendricks_beginning_intermediate_algebra_1e_ch1_3
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