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Lesson 5: Literal Equations and Real-World Applications — Practice Questions

  1. 1. The formula for distance is $d = rt$. If a car travels a distance of 210 miles at a constant rate of 35 miles per hour, how many hours does the trip take? The time is ___ hours.

  2. 2. The perimeter of a rectangular garden is 46 meters. If the width is 8 meters, what is the length of the garden? The length is ___ meters.

  3. 3. A formula is given by $A = xy$. If $A = 91$ and $x = 7$, what is the value of $y$? The value of $y$ is ___.

  4. 4. The perimeter of a picture frame is 50 inches. If its length is 15 inches, what is the width of the frame? The width is ___ inches.

  5. 5. The formula for the perimeter of a rectangle is $P = 2l + 2w$. Which equation correctly solves for the length, $l$?

    • A. $l = \frac{P - 2w}{2}$
    • B. $l = \frac{P + 2w}{2}$
    • C. $l = 2(P - 2w)$
    • D. $l = P - w$
  6. 6. A car rental company charges a flat fee of 25 dollars plus 2 dollars per mile. What is the total cost for a trip of 55 miles? ___ dollars

  7. 7. One number is 12 less than another number. Their sum is 78. If $x$ is the larger number, which equation correctly models this situation?

    • A. x - 12 = 78
    • B. x + (x + 12) = 78
    • C. x + (x - 12) = 78
    • D. 12x = 78
  8. 8. One number is 6 more than twice another number. If their sum is 48, what is the smaller number? ___

  9. 9. Two online tutoring services offer different payment plans. Service A is 50 dollars a month. Service B is 20 dollars a month plus 3 dollars per session, $s$. Which equation finds the number of sessions where both services cost the same?

    • A. 50 = 20 + 3s
    • B. 50s = 20 + 3
    • C. 50 + 20 = 3s
    • D. 50 = 20s + 3
  10. 10. Streaming Plan A costs 18 dollars per month. Plan B costs 8 dollars per month plus 2 dollars per movie rental. How many movies must be rented for the monthly cost of both plans to be equal? ___ movies