Question

Can some one show me how to do this please?

Peanuts worth $4/kg were mixed with almonds worth $6/kg to produce 12 kg of nuts worth $62.

A. Represent the unknowns above using the variables x and y. Show all your work.

B. Write an equation that models the relationships between te weights of the nuts in the mixture. Show all your work.

C. Write an equation that models the values of the nuts in the mixture. Show all your work.

D. Using the two equations above, write and solve the systems to find x and y. Show all your work.

Answer 1

To start this problem let us assume X kg of peanuts and mixed with Y kg of almonds. Now from the info in the question you can conclude 4X+12Y = 62 AND X+Y =12

Answer 2

Now you can solve from here to get the answer!

Answer 3

Yep, I'm with ankit042.

A. Pretty much, set the kilograms of peanuts to \(x\) and the kilograms of almonds to \(y\). This is just because you don't know how many kilograms you have of each, so you set them as variables to solve later.

B. The relationship between the weights, huh? Well, the kilograms of peanuts (\(x\)) and the kilograms of almonds (\(y\)) add up to be \(12\ [kg]\). In math (as opposed to English), that's \(x+y=12\ [kg]\).

C. A little more complicated than part B, but you can get it. You can use \(x\) and \(y\) like what they are. Pretend you know them, if that helps. And think of what you would do. You have the kilograms of peanuts, and you know they sell for $4/kg. So, \(x\) times $4\kg equals the money from peanuts. The almonds work similarly. And the money from each will add up to the total, $62. So \(\Large x\frac{$4}{[kg]}+y\frac{$6}{[kg]}=$62\)

D. Now you have two equations:\[x+y=12\ [kg]\]\[x\frac{$4}{[kg]}+y\frac{$6}{[kg]}=$62\]There are multiple approaches to solving these "systems of equations," but here I think it would be best to solve for a variable in the simpler equation, and substitute its value into the other equation. Like, find \(x\) in the top equation. Then plug what it's equal to in the bottom equation. Solve for the remaining variable, and you have one. Since you know that one, you can solve for the other in your original equation.