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Jerry has a large car which holds 2222 gallons of fuel and gets 2020 miles per gallon. Kate has a smaller car which holds 16.516.5 gallons of fuel and gets 3030 miles per gallon. If both cars have a full tank of fuel now and drive the same distance, in how many miles will the remaining fuel in each tank be the same?\newlineChoose 11 answer:\newline(A) 320320\newline(B) 325325\newline(C) 330330\newline(D) 335335

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Q. Jerry has a large car which holds 2222 gallons of fuel and gets 2020 miles per gallon. Kate has a smaller car which holds 16.516.5 gallons of fuel and gets 3030 miles per gallon. If both cars have a full tank of fuel now and drive the same distance, in how many miles will the remaining fuel in each tank be the same?\newlineChoose 11 answer:\newline(A) 320320\newline(B) 325325\newline(C) 330330\newline(D) 335335
  1. Calculate Total Distance: First, let's calculate the total distance each car can travel on a full tank.\newlineFor Jerry's car: Total distance = Tank capacity ∗* Mileage per gallon\newline= 2222 gallons ∗* 2020 miles/gallon\newline= 440440 miles
  2. Set Up Equation: For Kate's car: Total distance = Tank capacity ∗* Mileage per gallon\newline= 16.516.5 gallons ∗* 3030 miles/gallon\newline= 495495 miles
  3. Clear Fractions: Now, let's set up an equation to find the distance at which the remaining fuel in both tanks will be the same. Let xx be the distance driven by both cars. Jerry's car will have used x20\frac{x}{20} gallons, and Kate's car will have used x30\frac{x}{30} gallons. The remaining fuel in each car's tank will be their initial capacity minus the fuel used.\newlineFor Jerry's car: Remaining fuel = 22−x2022 - \frac{x}{20}\newlineFor Kate's car: Remaining fuel = 16.5−x3016.5 - \frac{x}{30}
  4. Distribute 6060: We want to find the distance xx where the remaining fuel is the same for both cars:\newline22−x20=16.5−x3022 - \frac{x}{20} = 16.5 - \frac{x}{30}\newlineTo solve for xx, we'll first clear the fractions by finding a common denominator, which is 6060 (the least common multiple of 2020 and 3030).\newlineMultiplying both sides by 6060 gives us:\newline60∗(22−x20)=60∗(16.5−x30)60*(22 - \frac{x}{20}) = 60*(16.5 - \frac{x}{30})
  5. Isolate x: Now, distribute the 6060 on both sides of the equation:\newline60×22−3×x=60×16.5−2×x60\times22 - 3\times x = 60\times16.5 - 2\times x\newline1320−3×x=990−2×x1320 - 3\times x = 990 - 2\times x\newlineTo isolate xx, we'll move the terms involving xx to one side and the constant terms to the other side:\newline1320−990=3×x−2×x1320 - 990 = 3\times x - 2\times x\newline330=x330 = x
  6. Final Result: We found that x=330x = 330 miles, which means that after driving 330330 miles, the remaining fuel in both Jerry's and Kate's cars will be the same.

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