4.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?
Please show work
Without algebra:
If there had only been 4-wheelers on the bridge there would have only been
32×4 or 128 tires. But there were 148 tires. Therefore the remaining 148-128
or 20 tires amounted to 10 extra pairs of tires which had to account for 10
6-wheelers that had an extra pair of tires. So there were 10 trucks and 32-10
= 22 cars.
By algebra:
x = the number of 4-wheelers
y = the number of 6-wheelers
Vehicle equation: x + y = 32
Tire(wheel equation: 4x + 6y = 148
Solve that system by substitution or elimination and get 22
4-wheelers and 10 6-wheelers.
Edwin