A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.

Question

zarkam21 · Answer

@Vocaloid

zarkam21 · Answer

@dude

Vocaloid · Answer

@shadow 
I'm going to bed soon (early shift tomorrow), would you mind taking a look at this

Shadow · Answer

So this problem is about a system of equations. We basically need to write two true equations for this scenario, and using those equations, solve for the unknown variables.

Shadow · Answer

Let x = the weight of the first bean in pounds 
Let y = the weight of the second bean in pounds

The first equation we can write is:
$$x + y = 120$$

This is because if the total mixture used is equal to 120, then we can say that its ingredients, x and y, constitute that total weight.

Shadow · Answer

Do you see the idea?

zarkam21 · Answer

yes

Shadow · Answer

We can actually make this a bit more efficient. Another way we can write this is that.

$$y = (120 - x)$$

Now for the second equation:

$$0.2x + 0.68y = 0.54(120)$$

What we're saying here is that the total pounds of x beans times its price + the total pounds of y beans times its price, = the total price of the mixture of beans times the total pounds of x + y beans.

Shadow · Answer

Using the y equation, we can make it so there's only one variable, and that we're able to solve:

$$0.20 + 0.68(120 - x) = 0.54(120)$$

Shadow · Answer

Do you think you got it from here?

Shadow · Answer

Fixed an error:

$$0.20x + 0.68(120 - x) = 0.54(120)$$

zarkam21 · Answer

x=35

Shadow · Answer

I got the same

zarkam21 · Answer

About this being reasonable, I think it would be right? 35

Shadow · Answer

Yes

zarkam21 · Answer

I think the answer to this question is reasonable. 35 is reasonable because it is not too expensive and not too cheap, the perfect price.

zarkam21 · Answer

Would this be ok to sum it up

Shadow · Answer

I think they're talking more so about your problem solving / thinking than the price of beans.

zarkam21 · Answer

okay thank you i have one more question that needs to be checked do you want me to open a new post

Shadow · Answer

Sure