bill and julio are selling wrapping paper for a school fundraiser. customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. bill sold 8 rolls of plain wrapping paper and 10 rolls of shiny wrapping paper for a total of $328. julio sold 9 rolls of plain wrapping paper and 2 rolls of shiny wrapping paper for a total of $184. find the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper

Plain rolls: $16

Shinny rolls: $20

Step-by-step explanation:

So, we have 2 equations to start with, let p = plain rolls and s = shinny rolls:

1) 8p + 10s = 328

2) 9p + 2s = 184

We need to isolate one variable, usually I go for the one with the lowest multiplicative ... so let's go for the '2s' and isolate the s from equation 2.

2s = 184 - 9p

3) s = (184 - 9p) / 2

And let's place that s equivalent into the first equation:

8p + 10 (184 - 9p) / 2 = 328

8p + 5 (184 - 9p) = 328

8p - 45p + 920 = 328

-37p = - 592

p = 16

Then we go into any of the 3 equations to get the value of s. Let's take the 3rd equation, it will be simpler:

s = (184 - 9p) / 2 = (184 - 9*16) / 2

s = (184 - 144) / 2 = 40/2 = 20

Then last step, we enter the values for s and p in one of the first equations to validate it. We haven't worked with first equation, so let's use that one:

8p + 10s = 328

8 (16) + 10 (20) = 328

128 + 200 = 328

328 = 328

Confirmed!