Answer: C. June 15th
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Step-by-step explanation:
Laura starts off with a balance of $606.40
This balance is in effect for x days, where x is some positive whole number between 1 and 30.
For the remaining 30-x days, her balance is 606.40-55.25 = 551.15 dollars after making the payment of $55.25
Here's a table to keep track of everything so far

where "Num Days" is shorthand for "number of days".
What we do is multiply the A and B column to form column C like this

Add up the stuff in column C
606.40x+551.15(30-x)
Then divide by 30 to compute the average daily balance

That average daily balance is plugged into this formula

where
- F = finance charge
- ADB = average daily balance
- APR = annual percentage rate
- n = number of days in the billing cycle
We are given the following
- F = 5.71
- APR = 0.1204
- n = 30
Plug in
and solve for x
So,


That value is approximate.
When rounding to the nearest whole number, we get x = 14.
Therefore, from June 1st to June 14th, Laura has a balance of $606.40
From June 15th to June 30th, she has a balance of $551.15
The payment was made on June 15th
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Checking the answer:
Here's the updated table with x replaced with 14. So x+1 = 14+1 = 15

Adding everything in column C gets us
8489.60+8818.40 = 17,308
Divide that over 30 days
(17,308)/30 = 576.93
Her average daily balance for the month of June is $576.93
Plug that into the formula mentioned to get the finance charge.

We get the correct finance charge of $5.71, so the answer has been confirmed.