Answer:
[tex]0\leq x\leq42[/tex]
Step-by-step explanation:
We have been given that checking account earnings at Long's Bank are expressed by the equation [tex]I=-0.06x+8.3[/tex]. The earnings at Fellow's Bank are modeled by [tex]I=-0.02x+6.6[/tex]. In both cases x is the number of checks written.
To find the number of checks that will generate more earnings at Long's bank then Fellow's Bank, we will set an inequality as:
[tex]-0.06x+8.3>-0.02x+6.6[/tex]
Now let us solve for x.
[tex]-0.06x+0.02x+8.3>-0.02x+0.02x+6.6[/tex]
[tex]-0.04x+8.3>6.6[/tex]
[tex]-0.04x+8.3-8.3>6.6-8.3[/tex]
[tex]-0.04x>-1.7[/tex]
Now let us divide both sides of our inequality by -0.04. Since dividing by a negative number swaps sign of inequality, so our inequality will be:
[tex]\frac{-0.04x}{-0.04}<\frac{-1.7}{-0.04}[/tex]
[tex]x<42.5[/tex]
Since the number of checks needs to be integer, so number of checks will be:
[tex]0\leq x\leq42[/tex]
Therefore, the number of checks between 0 to 42 checks will generate more earnings income at Long's Bank than Fellow's Bank.
