To take the neighbor's children to the movies. Mellie charges $5 for gas and $8 per hour spent with the children. Ron charges $3 for gas and $8.5 per hour spent with the children. If h represents the number of hours spent with the children, what are all the vlues of h for which Ron's total charge is greater than Mellie's total charge?

Options

A. `hlt3`
B. `3gthle4`
C. `4gehlt5`
D. `hgt4`

Explanation

To solve the problem, we need to compare the total charges of Mellie and Ron based on the number of hours spent with the children, represented by \( h \).

### Step 1: Write the expressions for total charges

**Mellie's total charge:**
- Gas: $5
- Charge per hour: $8
- Total charge for \( h \) hours:
\[ \text{Mellie's charge} = 5 + 8h \]

**Ron's total charge:**
- Gas: $3
- Charge per hour: $8.5
- Total charge for \( h \) hours:
\[ \text{Ron's charge} = 3 + 8.5h \]

### Step 2: Set up the inequality

We want to find when Ron's total charge is greater than Mellie's total charge:
\[ 3 + 8.5h > 5 + 8h \]

### Step 3: Simplify the inequality

To solve the inequality, we will first isolate the variable \( h \). Start by subtracting \( 8h \) from both sides:
\[ 3 + 8.5h - 8h > 5 \]
This simplifies to:
\[ 3 + 0.5h > 5 \]

Next, subtract 3 from both sides:
\[ 0.5h > 5 - 3 \]
This simplifies to:
\[ 0.5h > 2 \]

### Step 4: Solve for \( h \)

Now, divide both sides by 0.5 to isolate \( h \):
\[ h > \frac{2}{0.5} \]
This simplifies to:
\[ h > 4 \]

### Conclusion

The solution indicates that Ron's total charge is greater than Mellie's total charge when the number of hours \( h \) spent with the children is greater than 4.