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The problem states that Jack used $ \frac{2}{5} $ of his pocket money during recess. After school, he spent $10 on trading cards and was left with $5. We need to determine how much Jack spent during recess.

Let the total amount of Jack's pocket money be $ x $.

### Breakdown of the problem:
1. Jack spends $ \frac{2}{5} $ of $ x $ during recess. So, the amount he spends during recess is $ \frac{2}{5}x $.
2. After school, he spends an additional $10.
3. He has $5 left after all these expenses.

This gives us the equation for Jack's total expenses:

\[
x - \frac{2}{5}x - 10 = 5
\]

Simplifying this:

\[
x \left( 1 - \frac{2}{5} \right) - 10 = 5
\]

\[
x \left( \frac{3}{5} \right) - 10 = 5
\]

Adding 10 to both sides:

\[
\frac{3}{5}x = 15
\]

Now solve for $ x $:

\[
x = 15 \times \frac{5}{3} = 25
\]

So, Jack's total pocket money is $25.

### How much did Jack spend during recess?

He spent $ \frac{2}{5} $ of his pocket money during recess:

\[
\frac{2}{5} \times 25 = 10
\]

Thus, Jack spent **$10** during recess.

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Do you need further clarification or any more details?

Here are some related questions:
1. What would the result be if Jack had spent $ \frac{3}{5} $ of his pocket money instead?
2. If Jack had $30 as pocket money, how much would he spend during recess using the same fraction?
3. How would the problem change if Jack spent $15 after school instead of $10?
4. What fraction of his pocket money would Jack have left after spending during recess?
5. What would the equation look like if Jack had spent $ \frac{1}{4} $ of his money during recess?

**Tip:** Always translate word problems into equations based on the relationships they describe. This makes it easier to solve step-by-step.

Jack used 2/5 of his pocket money during recess. After school, he spent $10 on trading cards and had $5 left. How much did he spend during recess?

Find out how much Jack spent during recess using fractions and algebra. Jack used 2/5 of his pocket money during recess, spent $10 after school, and had $5 left. Learn how to break down this problem with equations and step-by-step calculations, suitable for students in Grades 6-8.

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