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gabbytheflower

During a 4th of July weekend, 32 vehicles became trapped on the Sunshine Skyway Bridge while it was being repaved. A recent city ordinance decreed that only cars with 4 wheels and trucks with six wheels could be on the bridge at any given time. If there were 148 tires that needed to be replaced to due to damage, how many cars and trucks were involved in the incident?

  • one year ago
  • one year ago

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  1. sandra
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    Basically you have two unknowns, so you need two equations in order to answer.

    • one year ago
  2. sandra
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    So let T be the number of trucks (with 6 wheels), and C be the number of cars (with 4 wheels)

    • one year ago
  3. sandra
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    C + T = 32

    • one year ago
  4. sandra
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    (total number of vehicles is 32)

    • one year ago
  5. sandra
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    AND 6T + 4C = 148 (the total number of tires ruined is 148, 6 per truck and 4 per car)

    • one year ago
  6. sandra
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    now you can solve using those two equations: 1. 4(C + T) = 4*32 2. 4C + 4T = 128 3. Now pull back the second equation - 6T + 4C = 148, notice that since you have 4C in step (2), you can just subtract to get (T) alone. 4. 6T + 4C = 148 - 4T + 4C = 132 --------------- 2T = 16 T = 8

    • one year ago
  7. sandra
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    That would mean there are 32 - 8 cars, which is 24 cars.

    • one year ago
  8. sandra
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    ooops, sorry , 4*32 = 128, copied it over wrong in step (4)

    • one year ago
  9. sandra
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    4. 6T + 4C = 148 - 4T + 4C = 128 --------------- 2T = 20 T = 10

    • one year ago
  10. sandra
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    there we go, got kicked out, and there are 32 - 10 cars

    • one year ago
  11. sandra
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    then check your answer - so 10 + 22 = 32 vehicles total (yay), and then 10*6 + 22*4 = 148 (148 tires total). So it works!

    • one year ago
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