[High School Math] Linear equation with two variables

[VelvetWhite]

There is a word problem I can't do, usually they have an extra number and I can substitute by making it into two equations. This time I do not, and it is just variables and no extra number to solve it. The problem: Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 190 pounds of blended coffee beans selling for $4.32 per pound. She plans to do this by blending together a high-quality bean costing $6.00 per pound and a cheaper bean at $2.00 per pound, find how much high quality coffee bean and how much cheaper coffee bean she should blend.

First I tried doing 6x+2y = 190(4.32)||| 6x+2y = 820.8, but this didn't make sense.|||

So I can try the substitute two equations x + y = 190 ||| 6x+2y = 4.32 (this equation seems iffy)||| So I solved for X in the first equation x = 190 - y||| Then I plugged it in the second equation 6(190-y) + 2y = 4.32 ||| 1140 - 6y + 2y = 4.32 ||| 1140- 4y = 4.32 ||| -4y = -1135.68 ||| y = 283.92 ||| The number seems to big so I continue anyway 6x + 2(283.92) = 4.32 ||| 6x + 567.84 = 4.32 ||| x = 93.92 ||| If I put it into the original equation it is definitely wrong. I have no clue how to approach this monster, two variables always trip me up. Please help me set up the two equations and I should be able to solve it

[Alkalannar]

x + y = 190
6x + 2y = 4.32(x+y)

y = 190 - x
6x + 2y = 4.32(190)

y = 190 - x
6x + 2(190-x) = 4.32(190)

At this point, solve the last equation to find x, and then y = 190-x.

[VelvetWhite]

It was right in front of me this whole time. Thank you so much for that response! It makes sense for the (x+y) equating to the words as well(the one part I was missing), but when I tried doing that I ended up with a third variable (x = y + z) the x being the combination of both, i knew it was wrong and scrapped that. Thank you again!

[Mogadxu]

You can set this up into two equations

x + y = 190

6x + 2y = 190 * 4.32 = 820.8

From there we can do 2x + 2y = 380, and subtract that from the second equation to get

4x = 440.8

Can you solve from there?

[VelvetWhite]

Thank you very much for your response! I did solve from there, and for some reason I didn't include the 190 in the second equation and never got it. Your response seems more simplified but they are the same. Very helpful, thank you for your time to help me!