Investing The expression 1000 ( 1.1 ) t 1000 . open 1.1 close to the t  represents the value of a $1000 investment that earns 10% interest per year, compounded annually for t years. What is the value of a $1000 investment at the end of each period?

24. 2 years
25. 3 years
26. 4 years
27. 5 years

See Problem 4.

Write an algebraic expression to model the total score in each situation. Then evaluate the expression to find the total score.

28. In the first set, the volleyball team made only 8 shots worth one point each.
29. In the last baseball game, there were two 3-run home runs and 4 hits that each scored 2 runs.

See Problem 5.

Simplify by combining like terms.

30. 5 a − a 5 eh minus eh
31. 5 + 10 s − 8 s 5 plus 10 s minus 8 s
32. − 5 a − 4 a + b negative 5 eh minus 4 eh plus b
33. 2a + 3b + 4a
34. 6r + 3s + 2s + 4r
35. 0.5 x − x 0.5 x minus x
36. 7 b − ( 3 a − 8 b ) 7 b minus open 3 eh minus 8 b close
37. 5 + ( 4 g − 7 ) 5 plus open 4 g minus 7 close
38. − ( 3 x − 4 y ) + x negative open 3 x minus 4 y close plus x

B Apply

Evaluate each expression for the given value of the variable.

39. x + 2 x − x − 1 ; x plus 2 x minus x minus 1 semicolon  x = 2
40. 2 z + 3 + 5 − 3 z ; z = − 3 2 z plus 3 plus 5 minus 3 z semicolon z equals negative 3
41. 3 ( 2 a + 5 ) + 2 ( 3 − a ) ; 3 open 2 eh plus 5 close plus 2 open 3 minus eh close semicolon  a = 4
42. 5 ( 2 k − 3 ) − 3 ( k + 4 ) 3 k + 2 ; k = − 2 fraction 5 . open , 2 k minus 3 , close . minus 3 . open , k plus 4 , close , over 3 k plus 2 end fraction . semicolon k equals negative 2
43. y 2 + 3 ; y = 7 y squared , plus 3 semicolon y equals square root of 7
44. 5 c 3 − 6 c 2 − 2 c ; c = − 5 5 , c cubed , minus 6 , c squared , minus 2 c semicolon c equals negative 5
45. Think About a Plan Tran's truck gets very poor gas mileage. If Tran pays $84 to fill his truck with gas and is able to drive m miles on a full tank, what expression shows his gas cost per mile?
    • What operation does “per” indicate?
    • Check your expression by substituting 200 miles for m. Does your answer make sense?

Simplify by combining like terms.

46. − a 2 + 2 b 2 + 1 4 a 2 negative , eh squared , plus 2 , b squared , plus , 1 fourth , eh squared
47. x + x 2 2 + 2 x 2 − x x plus , fraction x squared , over 2 end fraction , plus 2 , x squared , minus x
48. y 2 4 + y 3 + y 2 3 − y 5 fraction y squared , over 4 end fraction , plus , y over 3 , plus , fraction y squared , over 3 end fraction , minus , y over 5
49. − ( 2 x + y ) − 2 ( − x − y ) negative open 2 x plus y close minus 2 open negative x minus y close
50. x ( 3 − y ) + y ( x + 6 ) x open 3 minus y close plus y open x plus 6 close
51. 1 2 ( x 2 − y 2 ) − 5 2 ( x 2 − y 2 ) 1 half . open . x squared , minus , y squared . close . minus , 5 halves . open . x squared , minus , y squared . close

Write an algebraic expression to model each situation.

52. Class Project The freshman class will be selling carnations as a class project. What is the class's income after it pays the florist a flat fee of $200 and sells x carnations for $2 each?
53. Jobs You have a summer job at a car wash. You earn $8.50 per hour and are expected to pay a one-time fee of $15 for the uniform. If you work x hours per week, how much will you make during the first week?
54. Reasoning Suppose you need to subtract a from b but mistakenly subtract b from a instead. How is the answer you get related to the correct answer? Explain.

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