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  1. Subjects ›
  2. Prealgebra ›
  3. Question of the Day

Prealgebra Question of the Day

Prealgebra Question of the Day

Answer today's Prealgebra question, reveal the full explanation, then keep the streak going with a new question every day.

A parking garage charges a flat entrance fee plus an hourly rate. The total cost for parking 3 hours is 12,andthetotalcostforparking7hoursis12, and the total cost for parking 7 hours is 12,andthetotalcostforparking7hoursis20. If yyy represents the total cost and xxx represents the number of hours, which equation represents this situation?

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Question of the Day

A parking garage charges a flat entrance fee plus an hourly rate. The total cost for parking 3 hours is 12,andthetotalcostforparking7hoursis12, and the total cost for parking 7 hours is 12,andthetotalcostforparking7hoursis20. If yyy represents the total cost and xxx represents the number of hours, which equation represents this situation?

  1. y=2x+6y = 2x + 6y=2x+6 (correct answer)
  2. y=3x+3y = 3x + 3y=3x+3
  3. y=4x+0y = 4x + 0y=4x+0
  4. y=6x−6y = 6x - 6y=6x−6

Explanation: First find the slope: m=20−127−3=84=2m = \frac{20-12}{7-3} = \frac{8}{4} = 2m=7−320−12​=48​=2. Then use point-slope form with (3,12): y−12=2(x−3)y - 12 = 2(x - 3)y−12=2(x−3), which simplifies to y=2x+6y = 2x + 6y=2x+6. We can verify: when x=3x = 3x=3, y=2(3)+6=12y = 2(3) + 6 = 12y=2(3)+6=12 ✓, and when x=7x = 7x=7, y=2(7)+6=20y = 2(7) + 6 = 20y=2(7)+6=20 ✓. Choice B gives incorrect values (y=3(3)+3=12y = 3(3) + 3 = 12y=3(3)+3=12 works but y=3(7)+3=24≠20y = 3(7) + 3 = 24 \neq 20y=3(7)+3=24=20). Choice C gives y=4(3)=12y = 4(3) = 12y=4(3)=12 but y=4(7)=28≠20y = 4(7) = 28 \neq 20y=4(7)=28=20. Choice D gives y=6(3)−6=12y = 6(3) - 6 = 12y=6(3)−6=12 but y=6(7)−6=36≠20y = 6(7) - 6 = 36 \neq 20y=6(7)−6=36=20.