Question

samir works as a salesperson at an electronics store and sells phones and phone accessories. samir earns a $8 commission for every phone he sells and a $4 commission for every accessory he sells. on a given day, samir made a total of $216 in commission from selling a total of 39 phones and accessories. graphically solve a system of equations in order to determine the number of phones sold, x, and the number of accessories sold, y.

Explanation:

Step1: Define Variables and Equations

Let \( x \) be the number of phones sold and \( y \) be the number of accessories sold. We have two equations:

1. Total items sold: \( x + y = 39 \) (can be rewritten as \( y = -x + 39 \))
2. Total commission: \( 8x + 4y = 216 \) (divide by 4: \( 2x + y = 54 \), then \( y = -2x + 54 \))

Step2: Graph the Equations

• For \( y = -x + 39 \): When \( x = 0 \), \( y = 39 \); when \( y = 0 \), \( x = 39 \). Plot these points.
• For \( y = -2x + 54 \): When \( x = 0 \), \( y = 54 \); when \( y = 0 \), \( x = 27 \). Plot these points.

Step3: Find Intersection

The intersection of the two lines \( y = -x + 39 \) and \( y = -2x + 54 \) is found by solving the system. Set \( -x + 39 = -2x + 54 \), so \( x = 15 \). Substitute \( x = 15 \) into \( y = -x + 39 \), \( y = 24 \).

Answer:

The number of phones sold \( x = 15 \) and the number of accessories sold \( y = 24 \).