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Sharon is going to be participating in a long bike race soon. She needs to ride a total of at least 100100 kilometers today. She plans to do this by riding multiple laps on the Highland Loop, which is 3535 kilometers long, and the Pinehurst Loop, which is 4343 kilometers long.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of laps on the Highland Loop\newliney=y = the number of laps on the Pinehurst Loop\newlineChoices:\newline(A) 35x + 43y < 100\newline(B) 35x + 43y > 100\newline(C) 35x+43y≥10035x + 43y \geq 100\newline(D) 35x+43y≤10035x + 43y \leq 100

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Q. Sharon is going to be participating in a long bike race soon. She needs to ride a total of at least 100100 kilometers today. She plans to do this by riding multiple laps on the Highland Loop, which is 3535 kilometers long, and the Pinehurst Loop, which is 4343 kilometers long.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of laps on the Highland Loop\newliney=y = the number of laps on the Pinehurst Loop\newlineChoices:\newline(A) 35x+43y<10035x + 43y < 100\newline(B) 35x+43y>10035x + 43y > 100\newline(C) 35x+43y≥10035x + 43y \geq 100\newline(D) 35x+43y≤10035x + 43y \leq 100
  1. Define variables: Define the variables based on the given information.\newlineSharon needs to ride a total of at least 100100 kilometers today. She will ride laps on two different loops: the Highland Loop and the Pinehurst Loop.\newlineLet xx = the number of laps on the Highland Loop, which is 3535 kilometers long.\newlineLet yy = the number of laps on the Pinehurst Loop, which is 4343 kilometers long.
  2. Write expression: Write an expression for the total distance ridden.\newlineThe total distance Sharon rides will be the sum of the distances she rides on each loop.\newlineTotal distance = (Distance per lap on Highland Loop×Number of laps on Highland Loop)+(Distance per lap on Pinehurst Loop×Number of laps on Pinehurst Loop)(\text{Distance per lap on Highland Loop} \times \text{Number of laps on Highland Loop}) + (\text{Distance per lap on Pinehurst Loop} \times \text{Number of laps on Pinehurst Loop})\newlineTotal distance = 35x+43y35x + 43y
  3. Translate requirement: Translate the requirement into an inequality.\newlineSharon needs to ride at least 100100 kilometers, which means the total distance must be greater than or equal to 100100 kilometers.\newlineThe inequality that represents this situation is:\newline35x+43y≥10035x + 43y \geq 100
  4. Choose correct inequality: Choose the correct inequality from the given choices.\newlineThe correct inequality that describes Sharon's situation is (C)35x+43y≥100(C)35x + 43y \geq 100, which states that the total distance ridden on both loops must be at least 100100 kilometers.

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