Sure, let's go through the problem step by step.
1. Identify Known Values:
- Alan currently has [tex]$\$[/tex] 200$ saved.
- Alan earns [tex]$\$[/tex] 15$ per hour working as a lifeguard.
- Alan needs a total of [tex]$\$[/tex] 350$ to buy his surfboard.
2. Set Up the Equation:
- We are given the formula for the total money saved \( s \) after working \( h \) hours, which is \( s = 15h + 200 \).
- We need to find the number of hours \( h \) such that the total money saved \( s \) is [tex]$\$[/tex] 350$.
3. Substitute the Total Amount Needed into the Equation:
[tex]\[
350 = 15h + 200
\][/tex]
4. Solve for \( h \):
- Start by isolating \( h \) on one side of the equation. First, subtract 200 from both sides:
[tex]\[
350 - 200 = 15h
\][/tex]
- This simplifies to:
[tex]\[
150 = 15h
\][/tex]
- Next, divide both sides by 15 to solve for \( h \):
[tex]\[
h = \frac{150}{15}
\][/tex]
- Simplifies to:
[tex]\[
h = 10
\][/tex]
5. Interpret the Result:
- Alan needs to work for 10 hours in order to save the additional amount needed to reach [tex]$\$[/tex] 350$ for his surfboard.
In summary:
- Alan needs an additional [tex]$\$[/tex] 150$.
- To save this additional [tex]$\$[/tex] 150[tex]$, he needs to work for 10 hours at his hourly wage of $[/tex]\[tex]$ 15$[/tex] per hour.
