Writing a linear equation for a story problem.

Question

The Modern Grocery has cashews that sell for $4.75 a pound and peanut that sell for $2.50 a pound. How many of each must the grocer mix to get 90 pounds of mixture that he can sell for $3.00 per pound. Express the problem as a system of linear equations and solve using the method of your choice to find the solution of the problem.

Answer 1

Let c = cashews and p = peanuts here.

 

We know the prices of the different nuts. We also know that, combined, they will cost $270 (90 pounds*$3.00 per pound). Since cashews are being sold for $4.75 a pound, and peanuts for $2.50 a pound, you can write this as follows:

 

4.75c + 2.50p = 270              (1)

 

Then, for the second part, we can worry about weight. We know that, somehow, the two nuts together must equal 90 pounds. So we can represent the problem as follows:

 

c+p = 90                                (2)

 

So, we have our 2 equations. Once we have them, I will use the elimination method, multiplying equation (2) by -2.50 to get rid of the p variable, and leaving us with a way to isolate and solve for c.

 

4.75c + 2.50p = 270                           (1)

c+p = 90  (*-2.5)                               (2)

 

4.75c + 2.50p = 270

-2.5c-2.5p = -225

 

2.25c = 45

 

c= 20

p= 70

 

What does this mean? Out of the 90 pounds, 20 pounds of the nuts must be cashews to work, while the remaining weight (70 pounds) must be the peanuts. You can check the answer by the plugging that information back into the previous equations.

 

4.75(20)+2.50(70) = 95+175 = 270