Applications of Linear Systems Test

A plane traveled 2880 miles each way to Slotonville and back. The trip there was with the wind and took 15 hours. The trip back was into the wind and took 20 hours. Find the speed of the plane in still air, along with the speed of the wind.

Katlyn and Sara each improved their yards by planting rose bushes and shrubs. They purchased their supplies from the same store and paid the same per-unit price for each item. Katlyn spent $46 on 3 rose bushes and 4 shrubs. Sara spent $190 on 17 rose bushes and 5 shrubs. Find the cost of one rose bush and the cost of one shrub.

The senior classes at Delomme High School and Red High School planned separate trips to the City Park. The senior class at Delomme High rented and filled 4 vans and 13 buses with 676 students. Red High rented and filled 17 vans and 15 buses with 941 students. Every van had the same number of students in it as did the buses. Find the number of students in each van, along with the number of students on each bus.

One Sunday, a boat traveled to Lakeville and back. The distance was 144 miles each way downstream and back. The trip downstream took 8 hours. The trip back took 36 hours. Find the speed of the boat in still water and the speed of the current.

A chemical company manufactures three types of chemicals: Aplzeria (a pipe cleaner), Bellera (a detergent), and Clargentexson (a shower cleaner). Each day, legal restrictions require them to produce 10 more units of Clargentexson than the total of the other two types and twice as many Bellera units as Aplzeria units. They must produce a total of 490 units of the chemicals each day. How many units of each type can be made each day?