The expression
\[100 + 20m\] gives the volume of water, in liters, in Marcel’s pool after Marcel spends
\[m\] minutes filling his pool. What is the volume of water, in liters, in Marcel’s pool after he fills it for

\[5\dfrac{1}4\] minutes?

To solve this problem, we need to substitute the given time \( m = 5\dfrac{1}{4} \) minutes into the expression \( 100 + 20m \), which represents the volume of water in liters.

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \( 5\dfrac{1}{4} \) can be converted to an improper fraction as follows:
\[
5\dfrac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}
\]
So, \( m = \frac{21}{4} \).

### Step 2: Substitute \( m = \frac{21}{4} \) into the expression.
Now substitute \( m \) into the expression:
\[
100 + 20m = 100 + 20 \times \frac{21}{4}
\]

### Step 3: Simplify the expression.
Simplify the multiplication:
\[
20 \times \frac{21}{4} = \frac{20 \times 21}{4} = \frac{420}{4} = 105
\]

### Step 4: Add the result to 100.
Finally, add the result to 100:
\[
100 + 105 = 205
\]

### Final Answer:
The volume of water in Marcel’s pool after he fills it for \( 5\dfrac{1}{4} \) minutes is **205 liters**.

Would you like more details on any part of this problem?

Here are five related questions for further practice:
1. What is the volume of water after 7 minutes of filling?
2. How long does it take to reach 500 liters in the pool?
3. If the filling rate changes to 15 liters per minute, how would the expression change?
4. What is the volume of water after 8.5 minutes of filling?
5. How much water is added in the first 3 minutes?

**Tip:** When dealing with mixed numbers, always convert them to improper fractions for easier calculations.

The expression [100 + 20m] gives the volume of water, in liters, in Marcel’s pool after Marcel spends [m] minutes filling his pool. What is the volume of water, in liters, in Marcel’s pool after he fills it for [5\dfrac{1}4] minutes?

Discover how to calculate the volume of water in Marcel's pool using the expression 100 + 20m, after filling it for 5 1/4 minutes. This problem explores key algebraic concepts such as mixed number conversion and substitution, suitable for students in Grades 6-8.

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