Dewayne is comparing two checking accounts. One has a monthly fee of $7 and a per-check fee of $0.30, and the other has a monthly fee of $4 and a per-check fee of $0.40. What is the minimum number of checks Dewayne needs to write for the first bank to be a better option?
A. 29.
B. 28.
C. 30.
D. 31.
31
we want
7.00 + .30x < 4.00 + .40x
3.00 < .10x
30 < x
so, if Dewayne writes more than 30 checks, the first bank costs less.
check: at 30 checks, the two banks cost the same:
7.00 + .30*30 = 7+9 = 16.00
4.00 + .40*30 = 4 + 12 = 16.00
after that, since bank 1 charges less per check, it will be a better deal.
To determine the minimum number of checks Dewayne needs to write for the first bank to be a better option, we need to calculate the total cost for each bank at different check-writing frequencies and compare them.
Let's denote the number of checks as "x."
For the first bank with a monthly fee of $7 and a per-check fee of $0.30, the total cost can be calculated as:
Total_Cost_First_Bank = Monthly_Fee + (Per_Check_Fee * Number_of_Checks)
Total_Cost_First_Bank = $7 + ($0.30 * x)
Total_Cost_First_Bank = $7 + $0.30x
For the second bank with a monthly fee of $4 and a per-check fee of $0.40, the total cost can be calculated as:
Total_Cost_Second_Bank = Monthly_Fee + (Per_Check_Fee * Number_of_Checks)
Total_Cost_Second_Bank = $4 + ($0.40 * x)
Total_Cost_Second_Bank = $4 + $0.40x
To find the minimum number of checks for the first bank to be a better option, we need to find the value of "x" for which the total cost of the first bank is less than the total cost of the second bank.
Total_Cost_First_Bank < Total_Cost_Second_Bank
$7 + $0.30x < $4 + $0.40x
To solve this inequality, we'll subtract $0.30x and $4 from both sides:
$7 + $0.30x - $0.30x - $4 < $4 + $0.40x - $0.30x - $4
$3 < $0.10x
Then, we'll divide both sides by $0.10:
$3 / $0.10 < x
30 < x
So, Dewayne needs to write more than 30 checks for the first bank to be a better option. Therefore, the minimum number of checks Dewayne needs to write for the first bank to be a better option is 31.
The correct answer is:
D. 31.
To determine the minimum number of checks Dewayne needs to write for the first bank to be a better option, we'll compare the total costs of both banks for different numbers of checks written.
Let's start by calculating the total cost for each bank for a certain number of checks written.
For the first bank, the total cost (TC1) can be calculated using the formula:
TC1 = Monthly fee + (Per-check fee * Number of checks)
For the second bank, the total cost (TC2) can be calculated using the same formula:
TC2 = Monthly fee + (Per-check fee * Number of checks)
Given the details:
First Bank:
Monthly fee = $7
Per-check fee = $0.30
Second Bank:
Monthly fee = $4
Per-check fee = $0.40
We want to find the minimum number of checks for which the first bank's total cost (TC1) is less than the second bank's total cost (TC2).
For the first bank, the total cost (TC1) is:
TC1 = $7 + ($0.30 * Number of checks)
TC1 = $0.30 * Number of checks + $7
For the second bank, the total cost (TC2) is:
TC2 = $4 + ($0.40 * Number of checks)
TC2 = $0.40 * Number of checks + $4
To find the minimum number of checks that makes the first bank a better option, we need to set the TC1 less than TC2 and solve for the number of checks.
$0.30 * Number of checks + $7 < $0.40 * Number of checks + $4
Simplifying the equation:
$0.30 * Number of checks - $0.40 * Number of checks < $4 - $7
- $0.10 * Number of checks < - $3
Number of checks > - $3 / - $0.10
Number of checks > 30
Since we can't write a fraction of a check, the minimum whole number of checks Dewayne needs to write for the first bank to be a better option is 31.
Therefore, the answer is option D. 31.