Answer: One plain roll is 4 dollars and one shiny roll is 6 dollars.
Step-by-step explanation:
lets start by saying
rolls of plain wrapping paper = x
rolls of shiny wrapping paper = y
Kathryn sold 4 plain rolls and 3 shiny rolls for 34 dollars.
4x+3y=34
Eugene sold 4 plain rolls and 2 shiny rolls for 28 dollars
4x+2y=28
Both equations will look like this.
4x+3y=34
-1(4x+2y)=(28)-1
we can multiply the second equation by -1 to get y alone. (doesn't matter which equation). Once you do that, the positive 4x and the negative 4x cancel out, 3y-2y=1y and 34-28=6. you are left with
1y=6 so one shiny roll is 6 dollars.
now use that price to find the cost of the plain roll.
lets use Kathryn's equation
4x + 3(6)=34
4x + 18= 34
-18 -18
4x=16. Divide by 4 to find cost of one plain roll.
16÷4=4. One plain roll costs 4 dollars.
Lets check. Using Kathryn's equation,
4(4) + 3(6)=34
16+18=34
34=34. We are right.
180 - 64 = 116
116 / 2 = 58 :)
Check: 58 + 58 + 64 = 180
The ends of the rectangle = 10*10*2 = 200
The long sides and bottom of the rectangle = 12*10*3 = 360
Vertical end of the triangle = 5*10 = 50
The sides of the triangle = 12*5*1/2*2 = 60
Triangle slope = 13*10 = 130
Total = 200 + 360 + 50 + 60 + 130 =
800 in sq
