Charlotte works at an electronics store as a salesperson. Charlotte earns a 10% commission on the total dollar amount of all phone sales she makes, and earns a 4% commission on all computer sales. Charlotte had twice as much in computer sales as she had in phone sales and earned a total of $162 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Charlotte made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
c = 2p
0.10p + 0.04c = 162
To write a system of equations that can determine the dollar amount of phone and computer sales Charlotte made, let's define the variables:
Let P be the dollar amount of phone sales Charlotte made.
Let C be the dollar amount of computer sales Charlotte made.
Based on the given information, we know Charlotte earns a 10% commission on phone sales and a 4% commission on computer sales. We also know that she had twice as much in computer sales as she had in phone sales.
From this, we can create the following equations:
1. The commission earned on phone sales: 0.10P
2. The commission earned on computer sales: 0.04C
Since the commission earned from both phone and computer sales amounts to $162, we have the equation:
3. 0.10P + 0.04C = 162
Additionally, we know that Charlotte had twice as much in computer sales as phone sales, which can be represented as:
4. C = 2P
Therefore, the system of equations to determine the dollar amount of phone sales (P) and computer sales (C) would be:
Equation 1: 0.10P + 0.04C = 162
Equation 2: C = 2P