Jimmy has studied 22 hours over the last 10 days for the act. he studied either 2 hours a day or 3 hours a day. during the 10 day period, how many days did jimmy study for three hours a day? a) 1 b) 2 c) 3 d) 4

Let x represent the # of 2-hour days and y the # of 3-hour days.  Jimmy's study was spread over 10 days.  Thus, x + y must sum up to 10.  Also, 2x + 3y must sum up to 22 hours.

Our system now looks like this:

   x  +  y  = 10
 2x  +  3y = 22

Multiply the first equation by -2:  -2x - 2y = -20

Add the 2nd equation to this:

-2x - 2y = -20
2x  + 3y = 22

        y = 2       So Jimmy had 2 3-hour study days and 8 2-hour study days.

Note how these figures add up to 22:  6 + 16 = 22