120 -inch length of ribbon is to be cut into three pieces. the longest piece is to be 40 inches longer than the shortest piece, and the third piece is to be half the length of the longest piece. find the length of each piece of ribbon.

1. Let
Shortest piece = x
Longest piece = y
Third piece = z

2.
Shortest piece = x
Longest piece = 40 + x
Third piece = (40 + x)/2 OR 20 + 0.5x

3. Add all the expressions since you know that the total of all the pieces is 120 inches
40 + x + 20 + 0.5x + x = 120.

4. Add the whole numbers first, then add the variables.
40+20=60
x+0.5=2.5x
60+2.5x=120

5. To get rid of the 60, do the opposite of addition which is subtraction and subtract 60 from both sides.
2.5x=120-60
2.5x=60

6. Do the same but rather than addition, do the opposite of multiplying which is dividing, on both sides.
x=60/2.5
x=24

7.
Shortest piece = 64-40=24 inches
Longest piece = 24+40=64
Third piece = 64/2=32

There are 2 ways to do this with elimination method. You can either multiply the first equation by 6 or the second equation by 2. I think multiplying by 2 is easier therefore that's the way I'm going to show you.

x-2y=3001️⃣

6x-y-95=0 -simplify> 6x-y=952️⃣

multiply both sides of second equation by 2 to make 2y and eliminate

2️⃣*2

12x-2y=1903️⃣

Now we can eliminate!

3️⃣-1️⃣

12x-2y-(x-2y)=190-300

11x=-110

x=-10

Now substitute this back into either of the equations.

-10-2y=300

2y=-10-300

y=-155

So we get answers

x=-10

y=-155

Now check our work:

-10- 2*-155=-10+310=300 Correct!

6*-10- -155-95=155-95-60=60-60=0 Correct!

I really hope this helped you and if you have any more question about a step in how I got the answer, you can always ask in the comments and I will come answer whenever I see it!