Question Colton works at an electronics store as a salesperson. Colton earns a \( 7 \% \) commission on the total dollar amount of all phone sales he makes, and earns a \( 3 \% \) commission on all computer sales. Colton had twice as much in phone sales as he had in computer sales and earned a total of \( \$ 85 \) in commission. Write a system of equations that could made and the dollar ariount of computer sales he made. Define the variables that you use to write the system. Answer Attempt 1 out of 2

Let's define the variables to help us navigate Colton's commissions smoothly! Let \( p \) represent the dollar amount of phone sales and \( c \) represent the dollar amount of computer sales. Since Colton made twice as much in phone sales as in computer sales, we can express that as \( p = 2c \). Now, considering his commissions, we know he earns \( 7\% \) from phone sales and \( 3\% \) from computer sales. If we translate his total earnings to equations, we set up the commission equation as \( 0.07p + 0.03c = 85 \). So our system of equations is: 1. \( p = 2c \) 2. \( 0.07p + 0.03c = 85 \) Now let's find out how this all translates into real-world scenarios and what common pitfalls to avoid in such problems! Consider that commission structures like Colton’s are prevalent in many sales jobs. Commissions incentivize salespeople to push higher-value items, and understanding how to calculate one's earnings based on various percentages is key to personal finance. For example, similar strategies can be applied when selling cars or real estate, where commission can significantly influence both earnings and customer relations. One common mistake in these problems is overlooking the relationships between the variables. A clearer understanding often leads to more successful setups of equations. People sometimes jump into calculations without establishing the correct relationships first. It’s crucial to define how variables interact, as evident in Colton’s case with the phone-to-computer sales ratio! So always take a moment to outline what each variable represents before diving into solving the equations.