Final answer:
To determine the number of months after which Blake and Kevin have paid the same amount for their iPads, equations representing their payment plans can be set up and solved by equating the total amount paid by Blake to the total amount paid by Kevin.
Step-by-step explanation:
The student's question involves determining how many months Blake and Kevin will have paid the same amount for their iPads, given their different payment plans. To solve this, we can set up two equations to represent the total amount each person has paid over a certain number of months and find the point at which the two amounts are equal.
Let's assume x represents the number of months after which Blake and Kevin have paid the same total amount.
For Blake: Total Amount Paid by Blake = Initial Payment + (Monthly Payment × Number of Months)
Total Amount Paid by Blake = $100 + $25x
For Kevin: Total Amount Paid by Kevin = (Annual Payment × Number of Years) + (Monthly Payment × Number of Months)
Since Kevin pays annually and monthly, we need to convert the annual payments to a monthly equivalent to compare with Blake's payments. This is done by dividing the annual payment by 12.
Total Amount Paid by Kevin = ($250 ÷ 12) × x + $15x
To find the number of months where both have paid the same amount, we equate their total payments and solve for x:
$100 + $25x = ($250 ÷ 12) × x + $15x
After solving for x, we will find the number of months after which both Blake and Kevin have paid the same total amount for their iPads.