Solve for X: Finding Number of $4.50 Paper Packs Totaling $45

Q: Why do I set up the equation as 4.5x = 45?

Because the total cost equals price per pack times number of packs. Since each pack costs $4.50 and Lionel buys x packs, his total spending is 4.5x dollars.

Q: How do I divide 45 by 4.5 without a calculator?

Convert to whole numbers! Multiply both by 10: $ \frac{45}{4.5} = \frac{450}{45} = 10 $. This eliminates the decimal and makes division easier.

Q: What if the total cost wasn't evenly divisible?

You might get a decimal or fraction for x, which could mean partial packs. Always check if the context makes sense - you usually can't buy half a pack of paper!

Q: Can I check my answer a different way?

Yes! Ask yourself: "Does 10 packs at $4.50 each equal $45?" Calculate: 10 × $4.50 = $45.00 ✓

Q: What if I wrote the equation as x/4.5 = 45?

That's incorrect! This would mean x divided by 4.5 equals 45, giving x = 202.5. Always think: price per pack times number of packs equals total cost.

Linear Equations with Decimal Division

Lionel buys $x$ packs of paper.

The price of each pack is $4.5 and he pays a total of $45.

Calculate $x$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Price per package according to the given data

00:07 Let's mark the number of packages using the unknown X

00:10 The total amount paid

00:18 Isolate X

00:24 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

Lionel buys $x$ packs of paper.

The price of each pack is $4.5 and he pays a total of $45.

Calculate $x$ .

Step-by-step solution

To solve this problem, we'll use a step-by-step approach:

Step 1: Set up the equation based on the problem statement.
The total cost Lionel pays is given by the formula:

$4.5x = 45$

Here, $x$ is the number of packs Lionel buys, and $4.5 is the cost per pack.

Step 2: Solve for $x$ .
To find $x$ , divide both sides of the equation by 4.5:

$x = \frac{45}{4.5}$

Step 3: Perform the division.
Carrying out the division,

$x = \frac{45}{4.5} = 10$

Therefore, Lionel buys $x = 10$ packs of paper.

Final Answer

$x=10$

Key Points to Remember

Essential concepts to master this topic

Setup: Write equation as (price per pack) × (number of packs) = total cost
Technique: Divide both sides: $x = \frac{45}{4.5} = 10$
Check: Substitute back: 4.5 × 10 = 45 dollars ✓

Common Mistakes

Avoid these frequent errors

Dividing the wrong way around
Don't calculate $\frac{4.5}{45} = 0.1$ ! This gives the cost per dollar instead of packs bought. Always divide total cost by cost per pack: $\frac{45}{4.5} = 10$ .

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do I set up the equation as 4.5x = 45?

Because the total cost equals price per pack times number of packs. Since each pack costs $4.50 and Lionel buys x packs, his total spending is 4.5x dollars.

How do I divide 45 by 4.5 without a calculator?

Convert to whole numbers! Multiply both by 10: $\frac{45}{4.5} = \frac{450}{45} = 10$ . This eliminates the decimal and makes division easier.

What if the total cost wasn't evenly divisible?

You might get a decimal or fraction for x, which could mean partial packs. Always check if the context makes sense - you usually can't buy half a pack of paper!

Can I check my answer a different way?

Yes! Ask yourself: "Does 10 packs at $4.50 each equal $45?" Calculate:

10 × $4.50 = $45.00 ✓

What if I wrote the equation as x/4.5 = 45?

That's incorrect! This would mean x divided by 4.5 equals 45, giving x = 202.5. Always think: price per pack times number of packs equals total cost.

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