(Part 1) A local parking garage cost $12.00 a day, but if purchase a pass that costs $25.00 a month, the rate drops to $8 dollars a day.
After how many days would it be more cost effective to buy the pass?
You are saving $4 dollars a day buying the pass. The pass costs $25.00, so after 6 days you would save $4 x 6 = $24 dollars off the no pass rate and after 7 days you would save $4 x 7 = $28 off of the no pass rate. So, if you parked in the garage at least 7 days a month, you would benefit from purchasing the pass.
Write a formula that could be used to compare the cost with or without the pass.
*This problem is extremely hard for me to understand. Can you please break down so I can understand easily and especially if the wording is different. Thank you so much!*
12 d = 25 + 8 d
4 d = 25
d = 25/4 = 6 1/4 so if more than 6 days (7 or more)
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check
how much for 6 days?
without = 72
with = 25 + 48 = 73, so no pass
how much for 7 days
without = 84
with = 25 + 56 = 81, so yes, for 7 days cheaper with pass
At first I did not understand. Seeing it visual shed some light on the problem.
Thanks for sharing!
Sure, let's break down the problem step by step to make it easier to understand.
1. The cost of parking without the pass is $12 per day.
2. The cost of buying the pass is $25 per month.
3. If you buy the pass, the daily rate drops to $8 per day.
4. We want to figure out after how many days it would be more cost effective to buy the pass.
To solve this, we need to compare the cost of parking without the pass to the cost of parking with the pass.
Let's imagine parking for "x" number of days in a month, where "x" is the number of days you parked.
Without the pass, the cost would be $12 multiplied by "x" because you're paying $12 for each day.
With the pass, the cost would be $25 (the cost of the pass) plus $8 multiplied by "x" (the discounted daily rate).
So the total cost with the pass would be $25 + ($8 * x).
To determine when it's more cost effective to buy the pass, we need to find the number of days "x" that makes the total cost with the pass less than the total cost without the pass.
In equation form, we can write:
$25 + ($8 * x) < $12 * x
We can solve this inequality to find the value of "x" that satisfies it. By doing so, we can determine how many days you need to park in order for buying the pass to be more cost effective.
Let me know if you would like further assistance with solving the inequality.