Conert this to mathematical equation

Question

a grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 to make 100 pounds of mixture that cost $2.21 per pound. How much of each kind of nut is put into the mixture. 

Answer 1

While the posted answer is not incorrect, it is not the best way to solve the problem.  Why use 2 variables and a system of equations when you could simply use one variable and one equation!!!

 

Let P = pounds of peanuts;

since we know there is 100 pounds of the mixed nuts, if               p = lbs of peanuts         then.....

                                                                                     (100 - p)= lbs of walnuts         so.... 

 

(price of peanuts * lbs of peanuts) + (price of walnuts * lbs of walnuts) = total price         which can be written as...

 

               1.49 P  +  2.69 (100 - P) = 221   (now solve for p)

               1.49 P  +  269  - 2.69 P  = 221    (distribute and combine like terms)

               269 - 221  =  2.69 P  -  1.49 P     (get the variable terms on one side of equation/other terms-other side)

                 48 = 1.2 P    simplify and solve

                  48/1.2 = P

                     40 =p

 

And, if there are 40 lbs of peanuts, there must be 60 lbs of walnuts!

 

 

Answer 2

Let's first come up with a variable to call our inputs

 

Let P = # pounds of peanuts in the mixture

Let W = # pounds of walnuts in the mixture

 

We know that the mixture weighs 100 pounds so   P + W = 100

 

We know that the cost in dollars is 1.49P + 2.69W = 2.21(100)   because we have 100 pounds

at 2.21 per pound so

1.49P + 2.69W = 221

 

This gives us two equations which we can use to solve the problem

 

P + W = 100                     eqn 1

1.49P + 2.69W = 221        eqn 2

 

Let's solve eqn 1 for P in terms of W....  P = 100 - W

We can substitute that into eqn 2 to solve for W

 

1.49(100-W) + 2.69W = 221

149 - 1.49W + 2.69W = 221

1.2W = 221-149

1.2W = 72

W = 72/1.2

W = 60

 

We have 60 pounds of walnuts

 

P = 100-W = 100-60 = 40

 

We have 40 pounds of Peanuts