Elimination Story problem

Question

A merchant wants to mix pecans, which sell for $6 per pound, with cashews that sell for $12 per pound to make a 96-pound mixture he can export for $8 per pound. How many pounds of pecans and how many pounds of cashews should he use?

Answer 1

Hi Nicole, the way to work mixture problems is to set up a table with the information you know and then solve.

 

Let x represent the number of pounds of cashews you need in the mixture.

 

Then:

 

Product      Amount         Cost         Total

----------------------------------------------------

Pecans        96 - x             6         6 * (96 - x)

 

Cashews         x               12          12 * x

 

Mixture         96                8           8 * 96

 

We know the total for the pecans plus the total for the cashews will equal the total for the mixture.

 

Solve for x:

 

6 * (96 - x) + 12x  = 8 * 96

 

This will give you the number of pounds of cashews needed. To get the number of pecans needed, subtract the number of pounds of cashews from 96.

 

Questions?

 

 

Answer 2

p + c = 96

6p + 12c = 8(96)

 

I personally wouldn't use elimination, but I'm sure they are trying to keep it simple for you to learn. What we need is to make either the p's or c's to match up so they cancel out. For example, -2c + 2c = 0.

 

Let's multiply the top equation by -6. Now we have...

 

-6p - 6c = -576

6p + 12c = 768

 

Adding the two equations, we get...

 

6c = 192

c = 32

 

Since p + c = 92, p = 92 - c = 92 - 32 = 60.

 

32 lbs of cashews and 60 pounds of pecans.

 

Boom.