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gabbytheflower
 2 years ago
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?
gabbytheflower
 2 years ago
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?

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sandra
 2 years ago
Best ResponseYou've already chosen the best response.0Basically you have two unknowns, so you need two equations in order to answer.

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0So let T be the number of trucks (with 6 wheels), and C be the number of cars (with 4 wheels)

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0(total number of vehicles is 32)

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0AND 6T + 4C = 148 (the total number of tires ruined is 148, 6 per truck and 4 per car)

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0now 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

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0That would mean there are 32  8 cars, which is 24 cars.

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0ooops, sorry , 4*32 = 128, copied it over wrong in step (4)

sandra
 2 years ago
Best ResponseYou've already chosen the best response.04. 6T + 4C = 148  4T + 4C = 128  2T = 20 T = 10

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0there we go, got kicked out, and there are 32  10 cars

sandra
 2 years ago
Best ResponseYou've already chosen the best response.0then check your answer  so 10 + 22 = 32 vehicles total (yay), and then 10*6 + 22*4 = 148 (148 tires total). So it works!
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