Answered

Grayson charges [tex]\(\$35\)[/tex] per hour plus a [tex]\(\$35\)[/tex] administration fee for tax preparation. Ian charges [tex]\(\$45\)[/tex] per hour plus a [tex]\(\$15\)[/tex] administration fee. If [tex]\(h\)[/tex] represents the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

A. [tex]\(h \ \textless \ 2\)[/tex]
B. [tex]\(h \ \textgreater \ 2\)[/tex]
C. [tex]\(h \ \textless \ 5\)[/tex]
D. [tex]\(h \ \textgreater \ 5\)[/tex]



Answer :

GinnyAnswer
Let's analyze the charges for both Grayson and Ian to determine when Grayson's charges are higher than Ian's.

### Step-by-Step Solution:

1. Define the Cost Equations:
- Grayson's charges: [tex]\( 35h + 35 \)[/tex]
- Here, Grayson charges [tex]$35 per hour plus a $[/tex]35 administration fee.
- Ian's charges: [tex]\( 45h + 15 \)[/tex]
- Ian charges [tex]$45 per hour plus a $[/tex]15 administration fee.

2. Set Up the Inequality:
- We want to find out when Grayson's charges are more than Ian's, so we set up the inequality:
[tex]\[ 35h + 35 > 45h + 15 \][/tex]

3. Simplify the Inequality:
- First, subtract [tex]\(35h\)[/tex] from both sides to isolate the term with [tex]\(h\)[/tex] on one side:
[tex]\[ 35h + 35 - 35h > 45h + 15 - 35h \][/tex]
Simplifies to:
[tex]\[ 35 > 10h + 15 \][/tex]
- Next, subtract 15 from both sides to further simplify:
[tex]\[ 35 - 15 > 10h \][/tex]
Simplifies to:
[tex]\[ 20 > 10h \][/tex]

4. Solve for [tex]\(h\)[/tex]:
- To isolate [tex]\(h\)[/tex], divide both sides of the inequality by 10:
[tex]\[ \frac{20}{10} > h \][/tex]
Simplifies to:
[tex]\[ 2 > h \][/tex]
Which can also be written as:
[tex]\[ h < 2 \][/tex]

### Conclusion:

Grayson charges more than Ian when the number of hours of tax preparation is less than 2 hours.

Thus, the correct answer is:
[tex]\[ \boxed{h < 2} \][/tex]

Other Questions