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.
To find the range of checks for which a checking account at Long's Bank will generate more earnings income than one at Fellow's Bank, we need to compare the earnings equations for both banks.
Let I₁ represent the earnings at Long's Bank and I₂ represent the earnings at Fellow's Bank.
So we have:
I₁ = -0.06x + 8.3
I₂ = -0.02x + 6.6
To find the range of checks for which Long's Bank will generate more earnings income, we need to find the values of x for which I₁ > I₂.
Setting the two equations equal to each other and solving for x:
-0.06x + 8.3 = -0.02x + 6.6
0.04x = 1.7
x = 1.7 / 0.04
x = 42.5
So Long's Bank will generate more earnings income for a range of checks greater than 42.5 checks. Since you cannot have a fraction of a check, we can say that Long's Bank will generate more earnings income for 43 or more checks.