Math Problem Statement
Carson's Parking Garage charges $4.00 dollars for the first 3 hours plus $1.50 for each additional half hour. Ted only has $11.50 for parking. For how long can Ted park his car in this garage?
Solution
Let's break the problem down:
- The first 3 hours cost $4.00.
- After the first 3 hours, Ted is charged $1.50 for each additional half hour.
- Ted has $11.50 in total.
To find out how long Ted can park, we need to determine how many additional hours he can afford after the initial 3 hours.
Step 1: Calculate the remaining money after the first 3 hours
Ted pays $4.00 for the first 3 hours. So, the remaining money is:
Step 2: Determine how many half-hour blocks Ted can afford
Each additional half hour costs $1.50. The number of half-hour blocks Ted can afford is:
Step 3: Convert the half-hour blocks to hours
Since 5 half-hour blocks equal hours, Ted can afford an additional 2.5 hours.
Step 4: Calculate the total parking time
Ted can park for the initial 3 hours, plus the additional 2.5 hours:
Thus, Ted can park for 5.5 hours with his $11.50.
Would you like more details or have any questions?
Here are 5 related questions to expand your understanding:
- How much would Ted pay if he parked for 7 hours?
- What would be the maximum parking time if Ted had $20?
- How much more money would Ted need to park for 6 hours?
- If the cost per additional half hour increased to $2.00, how long could Ted park with $11.50?
- How would the total time change if the first 3 hours cost $5.00 instead?
Tip: Always calculate the base cost first and then the incremental costs when dealing with tiered pricing systems like this one.
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Math Problem Analysis
Mathematical Concepts
Arithmetic
Linear Equations
Unit Rate Calculation
Formulas
Total Cost = Initial Cost + (Cost per Half Hour × Number of Half-Hour Blocks)
Theorems
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Suitable Grade Level
Grades 5-7