24. Boating A boat is traveling in a river with a current that has a speed of 1.5 km/h. In one hour, the boat can travel twice the distance downstream as it can travel upstream. What is the boat's speed in still water?

25. Reasoning A student claims that the best way to solve the system below is by substitution. Do you agree? Explain.

    

26. Entertainment A contestant on a quiz show gets 150 points for every correct answer and loses 250 points for each incorrect answer. After answering 20 questions, the contestant has 200 points. How many questions has the contestant answered correctly? Incorrectly?

C Challenge

27. Number Theory You can represent the value of any two-digit number with the expression 10a + b, where a is the tens’ place digit and b is the ones’ place digit. For example, if a is 5 and b is 7, then the value of the number is 10(5) + 7, or 57. What two-digit number is described below?

    • The ones’ place digit is one more than twice the tens’ place digit.
    • The value of the number is two more than five times the ones’ place digit.
28. Mixed Nuts You want to sell 1-lb jars of mixed peanuts and cashews for $5. You pay $3 per pound for peanuts and $6 per pound for cashews. You plan to combine 4 parts peanuts and 1 part cashews to make your mix. You have spent $70 on materials to get started. How many jars must you sell to break even?

Standardized Test Prep

SAT/ACT

29. Last year, one fourth of the students in your class played an instrument. This year, 6 students joined the class. Four of the new students play an instrument. Now, one third of the students play an instrument. How many students are in your class now?

    1. 18
    2. 24
    3. 30
    4. 48

30. Which answer choice shows 2 x − y = z 2 x minus y equals z  correctly solved for y?

    6. y = 2x + z
    7. y = 2 x − z y equals 2 x minus z
    8. y = − 2 x + z y equals negative 2 x plus z
    9. y = − 2 x − z y equals negative 2 x minus z

Short Response

31. What is an equation of a line passing through the points (3, 1) and (4, 3) written in slope-intercept form?

Mixed Review

See Lesson 6-3.

Solve each system using elimination.

32. x + 3 y = 11 2 x + 3 y = 4 table with 2 rows and 1 column , row1 column 1 , x plus 3 y equals 11 , row2 column 1 , 2 x plus 3 y equals 4 , end table
33. 2 x + 4 y = − 12 − 6 x + 5 y = 2 table with 2 rows and 1 column , row1 column 1 , 2 x plus 4 y equals negative 12 , row2 column 1 , negative 6 x plus 5 y equals 2 , end table
34. 5 x + 8 y = 40 3 x − 10 y = − 13 table with 2 rows and 1 column , row1 column 1 , 5 x plus 8 y equals 40 , row2 column 1 , 3 x minus 10 y equals negative 13 , end table

Get Ready! To prepare for Lesson 6-5, do Exercises 35–37.

See Lesson 3-4.

Solve each inequality. Check your solution.

35. 3 a + 5 > 20 3 eh plus 5 greater than 20
36. 2 d − 3 ≥ 4 d + 2 2 d minus 3 greater than or equal to 4 d plus 2
37. 3 ( q + 4 ) ≤ − 2 q − 8 3 open q plus 4 close less than or equal to negative 2 q minus 8

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