Question
Question
Colton works at an electronics store as a salesperson. Colton earns a
commission on the total dollar amount of all phone sales he makes, and earns a
commission on all computer sales. Colton had twice as much in phone sales as he
had in computer sales and earned a total 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
Colton works at an electronics store as a salesperson. Colton earns a
commission on the total dollar amount of all phone sales he makes, and earns a
commission on all computer sales. Colton had twice as much in phone sales as he
had in computer sales and earned a total 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
Ask by Lynch Allan. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Let
Solution
To solve this problem, we need to define our variables and set up a system of equations based on the information provided.
Step 1: Define the Variables
Let:
-
= dollar amount of phone sales -
= dollar amount of computer sales
Step 2: Extract Known Conditions
- Colton earns a
commission on phone sales. - Colton earns a
commission on computer sales. - Colton had twice as much in phone sales as he had in computer sales:
. - Colton earned a total of
in commission.
Step 3: Set Up the Equations
From the information above, we can create the following equations:
-
The total commission earned from phone sales:
-
The total commission earned from computer sales:
-
The total commission earned is
: -
The relationship between phone sales and computer sales:
Step 4: Write the System of Equations
Now we can write the system of equations:
This system of equations can be solved to find the dollar amount of computer sales
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
Let’s define the variables to help us navigate Colton’s commissions smoothly! Let
Now, considering his commissions, we know he earns
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.
