Question

A grocer wants to make a 10-pound mixture of cashews and peanuts that he can sell for $3.29 per pound. If cashews cost $5.60 per pound and peanuts cost $2.30 per pound, how many pounds of each must he mix?

Ok, so...V.E.S.T stands for:
Variable
Equation
Solve
Try

Here is what I have so far, please re direct me if I am wrong.

V:

x = cashews
y = peanuts

So, now I wish to focus on the equation.

E:

x+y = $3.39(10)

^Correct so far?

Answer 1

vest?

Answer 2

i would say \(x+y=10\) if you need two variables ( you don't)

Answer 3

Yes, V.E.S.T...I guess so you remember the order how to perform each task. :P
And ok, x+y=10 makes sense.

Answer 4

here is the problem
you wrote "x = cashews" but x is not "cashews" you want the number of pounds of each so
"x = number of pounds of cashews" will be more like it

Answer 5

and "y = number of pounds of peanuts"
then it is more clear that \(x+y=10\) right?

Answer 6

yes, of course! That is what I had implied. :)

Answer 7

and then we need the pounds of each to add up to 10 pounds altogether yes?

Answer 8

don't imply it
say it
that makes for lots less confusion
then the cost of \(x\) pounds of cashews will be \(5.6x\) and the cost of \(y\) pounds of peanuts will be \(2.3y\)
the total cost will therefore be
\[5.6x+2.3y\] which must equal \(3.39\times 10\) giving you
\[5.6x+2.3y=33.9\]

Answer 9

Ok, I will from now on. I guess it does make it less confusing for both of us...

Answer 10

clear how to solve it right?
\[x+y=10\iff y=10-x\] solve
\[5.6x+2.3(10-x)=33.9\] or more simply
\[56x+23(10-x)=339\]

Answer 11

Alright, so now we have
5.6x + 2.3 y = 33.9
8.9 = 33.9 so...I'm missing something...

Answer 12

how do I determine the 10-x? That is where it get confusing to me like where did that come from?

Answer 13

23(10) = 230
23(x) = x ?

Answer 14

@satellite73 is teaching you the way he he learned this. He prefers to use only one variable when solving problems of this type even though it is more intuitive to use two variables since there are two main objects involved.

Answer 15

Ahhh... I can learn either way...I just need someone to explain it! lol!

Answer 16

the total is 10
if you have 4 pounds of cashews you have 6 of peanuts
if you have 3 pounds of cashews you have 7 of peanuts
if you have 2.5 pounds of cashews you have 7.5 of peanuts
if you have \(x\) pounds of cashews you have \(10-x\) of peanuts

Answer 17

That makes sense because you subtract x from 10 which leaves you with y. I understand that.

Answer 18

unless you want to use "elimination" which is a pita
you are going to end up solving
\[56x+23(10-x)=339\] no matter what you do

Answer 19

May I see it the other way for 2 variables?? The set up?

Answer 20

it is the same
\[x+y=10\\
5.6x+2.6y=33.9\]

Answer 21

I would prefer to use two variables because then you could set up two equations as follows:

Total Pounds of Nuts:
x + y = 10

Total Price of Nuts:
5.60x + 2.30y = 3.29(10)

Answer 22

As you can see, each equation actually means something that is clearly easy to understand intuitively.

Answer 23

Yes, I believe that is how I have been taught, however, I lost my reference sheet. :/

Answer 24

you really do not want to use elimination for this
you want to use substitution
@Hero i bent to the pressure and wrote that at the beginning too
even though i think it is silly
if you look up top you will see it

Answer 25

@satellite73, you're entitled to your opinion, but understand that not everyone sees things the same way you do.

Answer 26

Thank you, @satellite73 ! :) I see exactly what you mean, however, I believe my teacher is looking for @Hero example and I must show my work the way they taught or I get points off...:/ Which sucks really but...oh well

Answer 27

5.60(3) + 2.30(7) = 32.9
32.9 = 32.9

Answer 28

Well, if you want to learn how to do it using my setup, it involves taking the approach of solving systems of equations. You can setup the following system using my approach as follows:

x + y = 10
5.60x + 2.30y = 32.90


From there, you can multiply both sides of the first equation by 5.60 to get:

5.60x + 5.60y = 56.00
5.60x + 2.30y = 32.90


Then you can subtract the second equation from the first to eliminate x and end up with:

3.30y = 23. 10

and then divide both sides by 3.30 to isolate y
y = 23.10/3.30

Answer 29

And y = 7 as you discovered

Answer 30

And then from there it would be easy to see that x must be 3 since

3 + 7 = 10

Answer 31

Awesome! I just wanted to make sure I was doing it right and following the correct set up. :) Thank you @Hero ! What an appropriate user name by the way.

Answer 32

You're welcome.

Answer 33

There's something else you should know about me. I hate dealing with negatives so I avoid them as much as mathematically possible.