A piano teacher charges $30 for a one hour lesson, and $50 for a two hour lesson. She works for 25 hours in one week, and earns $690. Determine how many two hour lessons she gave.

Suppose the number of 2 hours lessons are x and 1 hour lessons are y; thus,

2x+y=25

50x+30y=690

to get the values of x and y we solve the quadratic equation given;

from the top equation:

y=25-2x ... i

substituting i in our second equation we get:

50x+30 (25-2x) = 690

50x+750-60x=690

-10x=-60

thus;

x=6

hence we conclude that the number of 2 hours classes are 6 hours