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

Price of each phone:
`\$9`

Price of each accessory:
`\$3.5`

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=(-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=(72)/(8)\\\\p=9`