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Stellar and indefatigable.
Imagine this: You’re calling a taxi, and the driver tells you, “It’s $5 for the first hour and $3 for each additional hour.” You might think, “Cool, that’s not too bad,” but then the SAT takes this simple concept and twists it into a math problem.
If test anxiety or SAT anxiety makes these questions feel impossible, don’t worry. Once you know the formula, these problems become way easier. Let’s break it down.
What Are These Problems Really About?
These SAT word problems are essentially linear models with a little extra twist. You’re usually given:
- A starting charge (like the cost of the first hour or two)
- A rate for each additional hour
Your job is to set up a simple equation that combines both parts.
Step 1: Understand the Problem
The problem will give you two types of charges:
- A fixed charge for the first hour (or first two or three hours)
- A variable charge for every hour after that
For example:
- Cost for the first hour: $5
- Cost for each additional hour: $3
The trick is to figure out how many hours fall into each category.
Step 2: Set Up the Equation
Let’s say the problem asks for the total cost if you use the service for h hours.
If the charge is $5 for the first hour and $3 for each additional hour, here’s how you break it down:
Example Problem
Question: A car rental company charges $10 for the first hour and $4 for each additional hour. How much will it cost to rent the car for 5 hours?
Step 1: Understand the Charges
- First hour: $10
- Each additional hour: $4
- Total hours: 5
Step 2: Set Up the Equation
Since the first hour is $10, we need to account for the additional 4 hours after that:
So, the total cost for 5 hours is $26.
Practice Problem
Question: A parking lot charges $8 for the first two hours and $2 for each additional hour. How much would it cost to park for 6 hours?
Step 1:
- First 2 hours: $8
- Each additional hour: $2
- Total hours: 6
Step 2:
Since the first 2 hours are $8, the next 4 hours are the additional cost:
So, the total cost for 6 hours is $16.
Test Anxiety Tip: Break It Down
When you see a word problem like this, don’t let SAT anxiety trick you into overthinking. Just remember:
- Identify the fixed charge.
- Identify the rate for each additional hour.
- Subtract the hours already covered by the fixed charge.
- Multiply the remaining hours by the rate.
- Add the fixed charge.
Keep it neat, take it one step at a time, and you’ll find the answer.
Final Thoughts
Word problems like these might seem complicated at first, but once you know how to set up the equation, it’s all downhill from there. Just remember to break down the problem, identify the parts, and you’ll be good to go.
Check back on this blog for more quick and easy math tips to help you tackle the SAT with confidence. You’ve got this!