Linear Equation: Calculate Hours of AC Usage at $1 per Hour = $180

Q: Why is the answer 180 hours and not something smaller?

Since Sarah pays $1 per hour and her total bill was $180, she must have used the AC for exactly 180 hours. The math is straightforward: 180 ÷ 1 = 180 hours.

Q: How do I know which number is the variable?

Look for what the problem is asking! The question asks "how many hours" the AC was on, so hours is your unknown variable. The $1 per hour and $180 total are given information.

Q: Is 180 hours realistic for one month?

Great question! There are about 720 hours in a month (30 days × 24 hours), so 180 hours means the AC ran about 25% of the time - which is reasonable for hot weather!

Q: What if the rate wasn't exactly $1 per hour?

The same method works! If it was $2 per hour, you'd write $ 2h = 180 $, then divide both sides by 2 to get h = 90 hours.

Q: Do I always write the equation as rate × time = total?

Yes! This is the standard format for unit rate problems. Rate per unit × number of units = total cost. It keeps your thinking organized and prevents setup errors.

Linear Equations with Direct Variable Solutions

Sarah pays $1 for every hour of air conditioning she operates. Last month she paid 180$.

Write an equation to find out how many hours the air conditioner was on that month.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many hours did the air conditioner run this month?

00:03 Price per hour according to the given data

00:06 Total hours according to the given data

00:09 Let's mark the number of monthly hours as unknown X

00:12 Hourly rate multiplied by number of hours equals total price

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Sarah pays $1 for every hour of air conditioning she operates. Last month she paid 180$.

Write an equation to find out how many hours the air conditioner was on that month.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Set up the equation based on the given information.
Step 2: Solve the equation to find the number of hours.

Now, let's work through each step:
Step 1: We know that Sarah pays $1 for every hour the air conditioner is on. Therefore, the equation representing the total cost is:
$180 = 1 \times h$

Step 2: Solve this equation for $h$ . Since $1 \times h = h$ , the equation simplifies to:
$h = 180$

Therefore, the solution to the problem is $h = 180$ .

Final Answer

180

Key Points to Remember

Essential concepts to master this topic

Setup: Cost per hour times number of hours equals total cost
Technique: Write $1 \times h = 180$ and solve for h
Check: Verify 1 × 180 = 180 hours gives correct total cost ✓

Common Mistakes

Avoid these frequent errors

Setting up the equation backwards
Don't write h = 1 × 180 or confuse hours with cost = wrong variable! This mixes up what you're solving for. Always identify what the variable represents first, then set up: rate × time = total cost.

Practice Quiz

Test your knowledge with interactive questions

Sarah pays $1 for every hour of air conditioning she operates. Last month she paid 180$.

Write an equation to find out how many hours the air conditioner was on that month.

FAQ

Everything you need to know about this question

Why is the answer 180 hours and not something smaller?

Since Sarah pays $1 per hour and her total bill was $180, she must have used the AC for exactly 180 hours. The math is straightforward: 180 ÷ 1 = 180 hours.

How do I know which number is the variable?

Look for what the problem is asking! The question asks "how many hours" the AC was on, so hours is your unknown variable. The $1 per hour and $180 total are given information.

Is 180 hours realistic for one month?

Great question! There are about 720 hours in a month (30 days × 24 hours), so 180 hours means the AC ran about 25% of the time - which is reasonable for hot weather!

What if the rate wasn't exactly $1 per hour?

The same method works! If it was $2 per hour, you'd write $2h = 180$ , then divide both sides by 2 to get h = 90 hours.

Do I always write the equation as rate × time = total?

Yes! This is the standard format for unit rate problems. Rate per unit × number of units = total cost. It keeps your thinking organized and prevents setup errors.

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Linear Equation: Calculate Hours of AC Usage at $1 per Hour = $180

Linear Equations with Direct Variable Solutions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the answer 180 hours and not something smaller?

How do I know which number is the variable?

Is 180 hours realistic for one month?

What if the rate wasn't exactly $1 per hour?

Do I always write the equation as rate × time = total?

🌟 Unlock Your Math Potential

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