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# Setting up a system of linear equations example (weight and price)

Practice writing a system of linear equations that fits the constraints in a word problem.

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• In D + L = 80, we have total no. of kilograms of beans but in 3D + 2L = 220 we are representing the total amount of money required to buy the beans, then how can we solve them if both the equations have different meanings? • I solved like this.
We have 2 equations.

1. D+L= 80
2. 3D+ 2L= 220

And find 'D' from the first equation.
D+L= 80
D= 80-L

Then, replace D in equation 2.
3D+ 2L= 220
3(80-L) + 2L = 220
240-3L+2L = 220
240-L = 220
-L= 220-240
L= 20

If L = 20 and L+D = 80,
D= 60

What about you? How do you solve? • For anyone trying to solve this. Here is one approach as mentioned previously; you can solve this by elimination of one variable so

D + L = 80
3D + 2L = 220

Lets try to eliminate one variable so that we can then plug it in and solve for the other variable.

You can add two equations since they have the same variables and go from there.

By looking at it you can see that by adding to equations you are not able to eliminate either D or L, for example adding the two gets you to 4D + 3L = 300

Since that’s the case you can do the following and multiply one or both equations with a constant to the point of being able to eliminate one variable.

Lets pick first equation and get it to the point of being able to eliminate 2L in the second equation. For that we would need to multiply by -2, which give us:

-2D -2L = -160

Now we can add two equations:

3D+2L=220
+
-2D-2L=-160
=
D=60

So D=60, following that

D + L = 80
60 + L = 80
L = 20

D = 60
L = 20

I am surprised elimination is not covered first for this problem. Looks like this topic is covered later however • • • • So there is this question:

Elliott has some yarn that she wants to use to make hats and scarves. Each hat uses 0.20 kilograms of yarn and each scarf uses 0.10 kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, and she wants to make a total of 20 items.

Let "h" be the number of hats Elliott makes and "s" be the number of scarves she makes.

Which system of equations represents this situation?

So it said these 2 equations:

H + S = 20
.1s = 2 x .2h

So I understand why the first equation makes sense, but I didn't quite understand the second one
(.1s = 2 x .2h). So in the answer, it said:

Each hat uses 0.20 kilograms of yarn, and h is the number of hats Elliott makes, so 0.2h represents how much yarn Elliott uses to make hats.
Similarly, each scarf uses 0.10 kilograms of yarn, and s is the number of scarves Elliott makes, so 0.1s represents how much yarn Elliott uses to make scarves.
Since she wants to use twice as much yarn for scarves as for hats, we need 0.1s to be twice as much as 0.2h:
0.1s = 2 x 0.2h

So my question is this. It says she wants to use TWICE as much yarn for scarves as for hats, so shouldn't the equation by 0.1s x 2 = 0.2h because she is using twice as much yarn for SCARVES as for hats? Makes sense? please answer asap!   • 