8-1 Solving Equations with Rational Coefficients
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1 1. 1.3c = = 7m p = A forest preserve rents canoes for $22.50 per hour. Corey has $90 to spend. Write and solve a multiplication equation to find how many hours he can rent a canoe h = 90; 4 h 11. The weight of an object on the Moon is one-sixth its weight on Earth. If an object weighs 54 pounds on the Moon, write and solve a division equation to find how much it weighs on Earth. ; 324 lb x = h = = 0.4j s = = 0.4r = 3y x = = 0.3t = 6g 1.4 esolutions Manual - Powered by Cognero Page 1
2 Rashid picked a total of 420 strawberries in hour. Write and solve an equation to find how many strawberries Rashid could pick in 1 hour. x = 420; 504 strawberries 28. Financial Literacy Marcus wants to save $378 in order to buy a new electronic keyboard. He plans to save $15.75 every week from his paycheck. Write and solve an equation to find how many weeks Marcus will need to save w = 378; 24 weeks 29. 5p 2p = = 4x + 3x (6y) = = 12( 3x) = k = n = = esolutions Manual - Powered by Cognero Page 2
3 35. n = 42. Use the table to help you write and solve an equation. 36. = x or = 9m 40. t = The sleeping heart rate of a black bear during hibernation is about of its summer rate. If the sleeping heart rate of a bear is 28 beats per minute during hibernation, find the summer sleeping heart rate. 70 bpm a. Jenna hikes at a steady rate of 2.5 miles per hour. How long will it take her to hike the Lone Star Trail? b. It takes Ming 4 hours to hike the Mallard Lake Trail. What is his average hiking rate? c. The round-trip distance of the Observation Point Trail is 56% of the round-trip distance of the Mystic Falls Trail. What is the round-trip distance of the Mystic Falls Trail? a. 2.5x = 4.8; 1.92 h b. 4x = 6.8; 1.7 mi/h c. 0.56x = 1.4; 2.5 mi 43. Use Math Tools A student solved the equation and found the solution m = 459. Use estimation to explain why the student s solution must be incorrect. Sample answer: The value of m is, which is approximately 1 5, so the answer should be close to Identify Structure Explain how to use the Multiplication Property of Equality to solve. Then explain how to solve the equation using the Division Property of Equality. To use the Multiplication Property of Equality, multiply each side of the equation by. To use the Division Property of Equality, divide each side by. esolutions Manual - Powered by Cognero Page 3
4 45. Multiple Representations Every autumn, the North American Monarch butterfly migrates up to 3000 miles to California and Mexico where it hibernates until early spring. The butterfly travels on average 52.5 miles per day. a. Symbols Write an equation that represents the distance d a butterfly will travel in t days. b. Table Use the equation to complete the table. 46. The formula for finding the area of a triangle is A = bh, where A represents the area, b represents the length of the base of the triangle, and h represents the height of the triangle. c. Graph Graph the points from the table on the coordinate plane. Graph time on the x-axis and distance on the y-axis. d. Graph Using the graph, estimate the number of days it will take the butterfly to travel 475 miles. e. Words How many days will it take a butterfly to travel 2100 miles? Which method did you use to solve the problem? a. d = 52.5t b. c. Write and solve equations to complete the table of values. 47. Model with Mathematics Write a real-world example that uses an equation containing a decimal and a fraction. Then find the solution. Sample answer: A shirt was on sale for half off. If the sale price was $15.60, find the original price; $ Find the Error Sam is solving. Find his mistake and correct it. d. about 9 days e. 40 days; See students work. He should have multiplied each side by 4; x = 80. esolutions Manual - Powered by Cognero Page 4
5 49. Justify Conclusions When you solve an equation of the form px = q, where p and q are rational numbers and p 0, is it ever possible for the solution to be 0? If so, when? If not, why not? Justify your conclusion. Yes; the solution is 0 when q = 0. In this case,. 50. Persevere with Problems If x = 3, what is the value of 7x + 13? Building on the Essential Question Suppose your friend says he can solve 3x = 15 by using the Multiplication Property of Equality. Is he correct? Justify your response. Sample answer: Yes; he can multiply each side of the equation by instead of dividing by During a vacation, the Morales family drove 63.2 miles in 1 hour. If they averaged the same speed during their trip, which equation can be used to find how far the Morales family drove in 6 hours? A B C 6x = 63.2 D 63.2x = 6 B 53. The solution of which equation is not graphed on the number line below? F 12.8 = 6.4 G 8.1x = 16.2 H 15 = 7.5x J 18.3x = 36.6 J 54. Ella paid $11.85 for 3 magazines. If each magazine was the same price, how much did each magazine cost? A $4.59 B $4.00 C $3.95 D $3.59 C 55. Short Response Stanley paid half of what Royce paid for his baseball glove. Royce paid $64.98 for his glove. Write and solve an equation to find how much Stanley paid for his glove. 2s = 64.98; $ x 5 = = 7 + p = y 9 31 esolutions Manual - Powered by Cognero Page 5
6 r = d 2.7 = t + ( 16) = p + = k = 64. d = 68. 3w + 4s w + 5s 2w + 9s (x + 3) 4x (2 + 3x) + 21x x x x 13x n 9 + 5n 9n (y + 8) 10y Find the values that complete the table below for y = 4x. Simplify each expression (t + 3) 5t x 12x 5x 67. 9p p 12p Gabriel is 12 years old, and his younger brother Elias is 2 years old. How old will each of them be when Gabriel is twice as old as Elias? Gabriel: 20; Elias: 10 esolutions Manual - Powered by Cognero Page 6
7 Find the value of each expression (4) (10 8) ( )( 2) ( ) [15 ( 9)] ( ) esolutions Manual - Powered by Cognero Page 7
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