Solve for X: Finding Camila's Balls When Total is 16 and Difference is 8

Q: How do I know David has x + 8 and not x - 8?

The key phrase is 'David finds 8 more balls than Camila'. 'More than' means addition, so David = Camila + 8. If it said 'fewer than', then you'd subtract.

Q: What if I get a decimal or fraction answer?

In this type of problem, you should get a whole number since we're counting balls. If you get a fraction, double-check your equation setup - you might have mixed up the variables.

Q: How do I check if my answer makes sense?

Ask yourself: Is my answer a positive whole number?Does David have exactly 8 more balls?Do their totals add up to 16? If all three are yes, you're correct!

Linear Equations with Two-Variable Word Problems

The total number of balls found by David and Camila is 16.

David finds 8 more balls than Camila.

Work out how many balls are found by Camila.

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The total number of balls found by David and Camila is 16.

David finds 8 more balls than Camila.

Work out how many balls are found by Camila.

Step-by-step solution

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

Step 1: Define the variable for Camila's balls.
Step 2: Set up an equation to sum their findings.
Step 3: Solve the equation for Camila's ball count.

Now, let's work through each step:

Step 1: Let $x$ be the number of balls Camila finds.
Step 2: According to the problem, David finds 8 more balls than Camila, so he finds $x + 8$ balls.
Therefore, the equation representing the total number of balls is:
$x + (x + 8) = 16$ .

Step 3: Simplify and solve for $x$ :

$x + x + 8 = 16$

Combine like terms:

$2x + 8 = 16$

Subtract 8 from both sides:

$2x = 8$

Divide both sides by 2:

$x = 4$

Therefore, the number of balls found by Camila is $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Variable Definition: Let x equal the unknown quantity you're solving for
Technique: David has x + 8 balls, so x + (x + 8) = 16
Check: Camila has 4, David has 12, and 4 + 12 = 16 ✓

Common Mistakes

Avoid these frequent errors

Setting up the equation incorrectly by confusing who has more
Don't write x - 8 for David's balls when he finds MORE than Camila = negative answer! This reverses the relationship and gives impossible results. Always read carefully: 'David finds 8 more' means David = x + 8.

Practice Quiz

Test your knowledge with interactive questions

$$ 11=a-16 $$

$a=\text{?}$

FAQ

Everything you need to know about this question

Why do I let x equal Camila's balls instead of David's?

You can choose either variable! But since we're asked to find Camila's balls, it's easier to let x represent what we're looking for. This way, our final answer is simply x.

How do I know David has x + 8 and not x - 8?

The key phrase is 'David finds 8 more balls than Camila'. 'More than' means addition, so David = Camila + 8. If it said 'fewer than', then you'd subtract.

What if I get a decimal or fraction answer?

In this type of problem, you should get a whole number since we're counting balls. If you get a fraction, double-check your equation setup - you might have mixed up the variables.

Can I solve this without algebra?

Yes! You could try different numbers: if Camila has 4, then David has 12, and 4 + 12 = 16 ✓. But algebra gives you the systematic approach that works for any similar problem.

How do I check if my answer makes sense?

Ask yourself:

Is my answer a positive whole number?
Does David have exactly 8 more balls?
Do their totals add up to 16?

If all three are yes, you're correct!

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