Question

Answer step by step

1.Avas school took a field trip. A total of 32 vehicles were needed for the trip.Some students took the bus, and some students car-pooled. There are 27 people on each bus and 3 people on each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?

Answer 1

Consider, please, this solution/explanation:
1. suppose, that number of cars is 'x', numbers of buses is 'y'.
2. according to the condition 'a total of 32', it means that x+y=32. This is the 1st equation.
3. according to the condition in one car are 3x persons, in one bus are 27y persons, and totaly 3x+27y=408 people. This is the 2d equation.
4. if to solve the system of two equations:
$\left \{ {{x+y=32} \atop {3x+27y=408}} \right. \ =\ \textgreater \ \ \left \{ {{x=19 (cars)} \atop {y=13(buses)}} \right.$

Answer: 13 - b., 19 - c.