Abigail works as a salesperson at an electronics store and sells phones and phone accessories. Abigail earns a $14 commission for each phone she sells and a $3.50 commission for each accessory she sells. On a given day, Abigail earned a total of $129.50 in commission and sold 7 more accessories than phones. She writes a system of equations that can be used to determine the number of phones sold and the number of accessories sold. She defines the variables that she will use to write the system.
Let P be the number of phones sold and A be the number of accessories sold.
The system of equations is:
P + A = total number of items sold
14P + 3.50A = total commission earned
Using the information given, we can write the equations:
P + A = total number of items sold
14P + 3.50A = 129.50
Since Abigail sold 7 more accessories than phones, we can also write the equation:
A = P + 7
To define the system of equations, we can start by defining the variables. Let's use the following variables:
P: Number of phones sold by Abigail
A: Number of accessories sold by Abigail
Now, we know that Abigail earns a $14 commission for each phone sold, so the commission earned from selling phones can be calculated as 14P. Similarly, she earns a $3.50 commission for each accessory sold, so the commission earned from selling accessories can be calculated as 3.50A.
According to the given information, Abigail earned a total of $129.50 in commission, so the total commission earned can be represented as 14P + 3.50A = 129.50.
Additionally, it is mentioned that Abigail sold 7 more accessories than phones, so we can express this relationship as A = P + 7.
With these equations, we have the system:
14P + 3.50A = 129.50
A = P + 7
These equations can be used to determine the number of phones sold (P) and the number of accessories sold (A) by solving the system.