Ayden’s 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 were 27 people on each bus and 3 people in each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?

Step-by-step explanation:

Let x be the number of buses for the trip.

Then (32 - x) is the number of cars for the trip.

We have 27x + 3(32 - x) = 408.

=> 27x + 96 - 3x = 408

=> 24x = 312

=> x = 13

Hence there are 13 buses and (32 - 13) = 19 cars.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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