https://file.aiquickdraw.com/mathbot/file/172910255127266gfpv0h.jpg

Let's define the target number of laps as \( x \).

### Step 1: Information from the problem
- After running some laps, Sam has completed **one-fifth of her target**, which means she has completed \( \frac{1}{5} \) of \( x \), or \( \frac{x}{5} \) laps.
- After running **2 more laps**, she has completed **one-quarter of her target**, which is \( \frac{x}{4} \) laps.

### Step 2: Setting up the equation
Let \( L_1 \) be the number of laps Sam initially ran before running the additional 2 laps:
- After the additional 2 laps, she has completed \( L_1 + 2 = \frac{x}{4} \).
- From the first part of the problem, \( L_1 = \frac{x}{5} \).

Substitute \( L_1 = \frac{x}{5} \) into the second equation:
\[
\frac{x}{5} + 2 = \frac{x}{4}
\]

### Step 3: Solving the equation
Now, solve for \( x \):
\[
\frac{x}{5} + 2 = \frac{x}{4}
\]
Subtract \( \frac{x}{5} \) from both sides:
\[
2 = \frac{x}{4} - \frac{x}{5}
\]
To combine the fractions on the right-hand side, find a common denominator:
\[
2 = \frac{5x}{20} - \frac{4x}{20}
\]
\[
2 = \frac{x}{20}
\]
Multiply both sides by 20 to solve for \( x \):
\[
x = 40
\]

### Conclusion:
Sam's target number of laps is **40**.

Would you like more details on the solution, or do you have any questions?

Here are 5 related questions you might explore:
1. How many laps had Sam run initially, before the additional 2 laps?
2. What fraction of the target had Sam completed after the 2 additional laps?
3. How would the target number of laps change if the fraction completed was different?
4. What if Sam had run 3 laps instead of 2 in the second part of the problem?
5. How would you set up the equation if the fractions in the problem were different, say one-third and one-fifth?

**Tip:** Always check your units and variables carefully when translating word problems into equations!

Sam runs around her athletics track. After running some laps, she has done one fifth of her target. After another two laps, she has done a quarter of her target. What is her target number of laps?

Learn how to solve a real-world problem involving running laps using fractions and equations. This problem explores algebraic concepts like fractions of a target, forming and solving equations. Suitable for students in Grades 6-8.

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