A construction company needs to transport a mix of small and large building materials to a job site. Each small container can hold 30 materials, and each large container can hold 50 materials. A total of 10 containers were sent, which can hold 400 materials altogether. Solve the system of equations to find the number of small and large containers sent.
Linear equation method
1. 30x + 50y = 400
2. x + y = 10
From equation 2, we can rewrite it as x = 10 - y and substitute into equation 1:
30(10 - y) + 50y = 400
300 - 30y + 50y = 400
20y = 100
y = 5
Substitute y back into x = 10 - y:
x = 10 - 5
x = 5
Therefore, 5 small containers and 5 large containers were sent.