Checking account earnings at Long's Bank are expressed by the equation, I=−0.06x+8.3
The earnings at Fellow's Bank are modeled by I=−0.02x+6.6
In both cases, x is the number of checks written.
For what range of checks will a checking account at Long's Bank generate more earnings income than one at Fellow's Bank? Show your work or explain how you got your answer.
(4 points)
To find the range of checks for which Long's Bank will generate more earnings income than Fellow's Bank, we need to find the values of x for which I (income) from Long's Bank is greater than I from Fellow's Bank.
Let's set up the inequality:
-0.06x + 8.3 > -0.02x + 6.6
Let's simplify the inequality:
-0.06x + 0.06x > 6.6 - 8.3
0 > -1.7
Since this statement is true for all values of x, there is no specific range of checks for which Long's Bank generates more earnings income than Fellow's Bank. Long's Bank will always generate more earnings income.
Alternatively, if we want to find the values of x where Long's Bank generates more income than Fellow's Bank, we can subtract the two equations:
(-0.06x + 8.3) - (-0.02x + 6.6) > 0
-0.06x + 0.02x + 8.3 - 6.6 > 0
-0.04x + 1.7 > 0
Since the coefficient of x is negative, the inequality sign flips when dividing by -0.04:
x < 1.7 / 0.04
x < 42.5
Therefore, for any number of checks written less than 42.5, Long's Bank will generate more earnings income than Fellow's Bank.