Mammoth Printing Company charges a fee of $28 to print an overized poster, and $7 for each color of ink used in the poster. Colossal Printing charges a fee of $34 to print an oversized poster and $5.50 for each color of ink used. If x represents the number of colors of ink used to print poster, what are all the values of x for which Mammoth Printing Company would charges more to print the poster than Colossal Printing?

Options

A. `xlt4`
B. `2lexle4`
C. `4lexle7`
D. `xgt4`

Answer

To solve the problem, we need to compare the charges of Mammoth Printing Company and Colossal Printing Company based on the number of colors of ink used, represented by \( x \).

1. **Define the charges for each company:**
- Mammoth Printing Company charges a fixed fee of $28 plus $7 for each color of ink used. Therefore, the total charge can be expressed as:
\[ \text{Charge}_{\text{Mammoth}} = 28 + 7x \]
- Colossal Printing Company charges a fixed fee of $34 plus $5.50 for each color of ink used. Thus, the total charge can be expressed as:
\[ \text{Charge}_{\text{Colossal}} = 34 + 5.5x \]

2. **Set up the inequality:**
We want to find the values of \( x \) for which Mammoth Printing charges more than Colossal Printing. This can be expressed as:
\[ 28 + 7x > 34 + 5.5x \]

3. **Rearrange the inequality:**
To solve the inequality, we will first move all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 5.5x \) and \( 28 \) from both sides:
\[ 7x - 5.5x > 34 - 28 \]
Simplifying this gives:
\[ 1.5x > 6 \]

4. **Solve for \( x \):**
Now, divide both sides by \( 1.5 \) to isolate \( x \):
\[ x > \frac{6}{1.5} \]
Calculating the right side gives:
\[ x > 4 \]

5. **Conclusion:**
Therefore, the values of \( x \) for which Mammoth Printing Company charges more than Colossal Printing Company are:
\[ x > 4 \]