Question

Madison works as a salesperson at an electronics store and sells phones and phone accessories, and makes a fixed commission for each phone sale and a different fixed commission for each accessory sale. Yesterday Madison sold 8 phones and 10 accessories and made a total commission of $107. Today she sold 4 phones and 23 accessories and made a total commission of $116.50. Determine the price of each phone and the price of each accessory.

Answer 1

Answer:

Price of each phone: $\ 9$

Price of each accessory: $\ 3.5$

Step-by-step explanation:

Let be "p" the  price in dollars of each phone and "a" the price in dollars of each accessory.

Set up a system of equations:

$\left \{ {{8p+10a=107} \atop {4p+23a=116.50}} \right.$

You can use the Elimination Method to solve the system.

Multiply the second equation by -2 and add both equations:

$\left \{ {{8p+10a=107} \atop {-8p-46a=-233}} \right.\\............................\\-36a=-126\\\\a=\frac{-126}{-36}\\\\a=3.5$

Substitute the value of "a" into the first equation and solve for "p":

$8p+10(3.5)=107\\\\8p=107-35\\\\p=\frac{72}{8}\\\\p=9$