Suppose contact lenses cost $300 for a year’s supply or $30 for a month’s supply. Which is less expensive to order per year, paying for 12 months at one time or paying for 1 month at a time?(1 point)
month(s) at a time
Give a simple and correct answer
To find out which option is less expensive per year, let's compare both options.
Paying for a year's supply at one time:
Cost per month = $300 / 12 months = $25 per month
Paying for a month's supply at one time:
Cost per month = $30
From the calculations above, we can see that paying for a year's supply at one time costs $25 per month, while paying for a month's supply at one time costs $30 per month.
Therefore, it is less expensive to order contact lenses by paying for 12 months at one time.
how many months at a time
To determine how many months at a time is less expensive, we need to compare the cost of different options.
Suppose we want to compare the cost of ordering contact lenses for n months at a time. The cost for a year's supply is $300, which is equivalent to ordering for 12 months at a time.
Thus, the cost for n months at a time can be calculated as follows:
Cost for n months = ($30 × n)
We need to find the value of n for which the cost for n months at a time is less than $300.
($30 × n) < $300
Dividing both sides by $30, we have:
n < $300 / $30
n < 10
This means that ordering contact lenses for fewer than 10 months at a time would be less expensive than ordering for a year's supply.
To determine which option is less expensive per year, we can compare the total cost of ordering 12 months at one time with the total cost of ordering 1 month at a time.
For 12 months at one time:
Total cost = $300
For 1 month at a time:
Total cost = $30 x 12 months = $360
Therefore, ordering 12 months at one time is less expensive, with a total cost of $300.