To determine the volume of water in Marcel's pool after he fills it for [tex]\(5 \frac{1}{4}\)[/tex] minutes, let's proceed step-by-step:
1. Understand the Expression: The expression [tex]\(100 + 20m\)[/tex] gives the volume of water (in liters) in Marcel's pool after [tex]\(m\)[/tex] minutes of filling. Here, 100 liters is the initial volume of water in the pool.
2. Identify Values: We are given that Marcel spends [tex]\(5 \frac{1}{4}\)[/tex] minutes filling the pool. Express this mixed number as an improper fraction or a decimal:
[tex]\[
5 \frac{1}{4} = 5 + \frac{1}{4} = 5 + 0.25 = 5.25 \text{ minutes}
\][/tex]
3. Substitute the Time: Substitute [tex]\(m = 5.25\)[/tex] into the expression [tex]\(100 + 20m\)[/tex]:
[tex]\[
\begin{align*}
100 + 20m &= 100 + 20 \times 5.25
\end{align*}
\][/tex]
4. Calculate the Product: Multiply 20 by 5.25 to find the additional volume of water added:
[tex]\[
20 \times 5.25 = 105 \text{ liters}
\][/tex]
5. Add the Initial Volume: Add the additional volume to the initial 100 liters:
[tex]\[
100 + 105 = 205 \text{ liters}
\][/tex]
Therefore, the volume of water in Marcel's pool after he fills it for [tex]\(5 \frac{1}{4}\)[/tex] minutes is [tex]\(205\)[/tex] liters.
