Word problem

Question

The owner of Nuts2U Snack Shack mixes cashews worth $5.50 per pound with peanuts worth $2.00 per pound to get a half pound, mixed-nut bag worth $1.80. How much of each kind of nut is included in the mixed bag?

 

How do I set it up step by step? 

Answer 1

C is the amount of cashews in pounds

P is the amount of peanuts in pounds

 

C + P = 1/2

 

$5.50*C + $2*P = (1/2)*$1.80 = $0.90

 

solving the first equation for P and multiplying the second equation by 10 to clear away the decimals.

 

P = 1/2 - C 

 

55C + 20P = 9

 

 

Substituting the first equation into the second...

 

55C + 20( 1/2 - C) = 9

 

55C + 10 - 20C = 9

 

35C + 10 = 9

 

35C = 9 -10

 

35C = -1

 

C = -1/35 = -2/70

 

-1/35 + P = 1/2

 

-2 + 70p = 35

 

70p = 37

 

p = 37/70

 

check:

 

  (37/70)*$2 + (-1/35)*$5.50 =   37/35 - 5.50/35 = 31.50/35 = 0.9 = 1/2*$1.80

 

So it checks. Therefore, something in the statement of the problem is

incorrect, which causes the negative answer.

 

Please repost