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
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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
To find the range of checks for which a checking account at Long's Bank generates more earnings income than at Fellow's Bank, we need to compare the two equations and solve for x.
I = -0.06x + 8.3 (Earnings at Long's Bank)
I = -0.02x + 6.6 (Earnings at Fellow's Bank)
We can set the two equations equal to each other to find the break-even point:
-0.06x + 8.3 = -0.02x + 6.6
Now, we can solve for x:
-0.06x + 0.02x = 6.6 - 8.3
-0.04x = -1.7
x = (-1.7)/(-0.04)
x = 42.5
Therefore, Long's Bank will generate more earnings income than Fellow's Bank if the number of checks written is greater than 42.5. However, since we cannot have half a check, we take the range to be x > 42.