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We are given that:

- Joey earns $12 an hour and gets a raise of $1.50 every six months.
- Blake earns $16 an hour and gets a raise of $0.50 every six months.

The goal is to determine the equation that represents the number of six-month intervals, $x$, it will take for Joey's hourly wage to equal Blake's.

### Joey's hourly wage:
Joey's initial wage is $12 per hour. After each six-month interval, his wage increases by $1.50, so his wage after $x$ six-month intervals is:
\[
12 + 1.5x
\]

### Blake's hourly wage:
Blake's initial wage is $16 per hour. After each six-month interval, his wage increases by $0.50, so his wage after $x$ six-month intervals is:
\[
16 + 0.50x
\]

### Setting Joey's and Blake's wages equal:
We need to find when Joey's wage equals Blake's wage, so we set the two expressions equal to each other:
\[
12 + 1.5x = 16 + 0.50x
\]

This corresponds to option **C** in the choices given.

Would you like more details on solving the equation? Here are some related questions:

1. How can we solve the equation $12 + 1.5x = 16 + 0.50x$?
2. What is the interpretation of the variable $x$ in this context?
3. How do the wage increments affect the number of six-month intervals needed?
4. How can this type of equation be applied to other real-life salary growth problems?
5. How would the answer change if Blake’s raise was different?

**Tip:** To solve equations efficiently, always isolate the variable you're solving for by simplifying both sides step-by-step.

Joey earns $12 an hour. Blake earns $16 per hour. Joey receives a raise of $1.50 every six months, and Blake receives a raise of $0.50 every six months. Which equation can be used to find x, the number of six-month intervals it will take Joey to earn hourly the same as Blake?

Learn how to solve the equation 12 + 1.5x = 16 + 0.50x to determine how many six-month intervals it will take for Joey to earn the same hourly wage as Blake. The problem demonstrates basic algebraic concepts involving linear equations and wage growth. Suitable for students in Grades 7-9.

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