Scarlett works as a salesperson at an electronics store and sells phones and phone accessories. scarlett earns a $14 commission for every phone she sells and a $3 commission for every accessory she sells. on a given day, scarlett made a total of $344 in commission from selling a total of 45 phones and accessories. determine the number of phones sold and the number of accessories sold.

19 phones and 26 accessories

Step-by-step explanation:

What we need here is to work with a two-equation system, where one equation corresponds to income and the other to the amounts sold.

First, lets think on the amounts. She sold a p amount of phones and an a amount of accessories, such that in total she sold 45 items. So:

a + p = 45 [equation 1]

Then, she made a total money of $344, for selling this 45 items. With prices of $3 for accessories and $14 for phones. The equation is:

3a + 14 p = 344 [equation 2]

If we take equation 1 en get the value of a, by subtracting p en both sides:

a + p - p = 45 - p

a = 45 - p [equation 1']

If we pick this last equation and replace in equation 2 we have:

3a + 14 p = 344

3 (45-p) + 14p = 344

135 - 3p + 14p = 344

135 + 11 p = 344

Subtracting 135 in both sides:

135 -135 + 11p = 344 - 135

11p = 209

Dividing by 11 in both sides:

11p/11 = 209/11

p = 19

So, Scarlett sold 19 phones. If we replace it in equation 1:

a + 19 = 45

Subtracting 19 in both sides:

a = 26

She also sold 26 accessories.