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!