24 Chapter 1Solving Linear Equations 28. PROBLEM SOLVING One serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams of protein from other sources. How many grams of protein do you need daily?USING STRUCTURE In Exercises 29 and 30, nd the value of r. 29. 8(x + 6) 10 + r 3(x + 12) + 5x 30. 4(x 3) r + 2x 5(3x 7) 9xMATHEMATICAL CONNECTIONS In Exercises 31 and 32, the value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x. Then nd the surface area and volume of the cylinder.31. x cm2.5 cm 32. x ft7 ft15 33. MODELING WITH MATHEMATICS A cheetah that is running 90 feet per second is 120 feet behind an antelope that is running 60 feet per second. How long will it take the cheetah to catch up to the antelope?
(See Example 4.) 34. MAKING AN ARGUMENT A cheetah can run at top speed for only about 20 seconds. If an antelope is too far away for a cheetah to catch it in 20 seconds, the antelope is probably safe. Your friend claims the antelope in Exercise 33 will not be safe if the cheetah starts running 650 feet behind it. Is your friend correct? Explain.REASONING In Exercises 35 and 36, for what value of a is the equation an identity? Explain your reasoning. 35. a(2x + 3) 9x + 15 + x 36. 8x 8 + 3ax 5ax 2a37.REASONING Two times the greater of two consecutive integers is 9 less than three times the lesser integer. What are the integers?38. HOW DO YOU SEE IT? The table and the graph show information about students enrolled in Spanish and French classes at a high school.Studentsenrolled this yearAverage rate of changeSpanish3559 fewer students each yearFrench22912 more students each yearPredicted LanguageClass Enrollment EnrollmentStudents enrolled0150200250300350400yYears from now12345789106xSpanishFrench a. Use the graph to determine after how many years there will be equal enrollment in Spanish and French classes. b. How does the equation 355 9x 229 + 12x relate to the table and the graph? How can you use this equation to determine whether your answer in part (a) is reasonable? 39. WRITING EQUATIONS Give an example of a linear equation that has (a) no solution and (b) innitely many solutions. Justify your answers. 40. THOUGHT PROVOKING
x + 32x + 13x
Draw a different gure that has the same perimeter as thetriangle shown. Explain why your gure has the same perimeter.Maintaining Mathematical ProficiencyMaintaining Mathematical ProficiencyOrder the values from least to greatest. (Skills Review Handbook) 41. 9, 4 , 4, 5, 2 42. 32 , 22, 16, 21 , 10 43. 18, 24 , 19, 18 , 22 44. 3 , 0 , 1, 2 , 2Reviewing what you learned in previous grades and lessons