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Question

Big Dog sells a beef-based dog food for $2.30 per pound and a lamb-based food for $3.80 per pound. They sell a mixture of the two kinds of food for $2.90 per pound. Let b represent the amount of beef food the company uses in 8 pounds of the mixture.

Answer 1

Is the question asking for the amount of beef (in pounds) in the mixture?  If so, here's how you calculate it:

 

Let B = % beef and L = % lamb in mixture (both expressed in decimal form)

 

$2.30*B + $3.80*L = $2.90

B + L = 1   (% of beef + % of lamb = 100 % assuming that there is nothing else in the mixture, and expressed in decimal form)

 

Solve for B.

 

Rearrange 2nd equation:  L = 1 - B

Substitute L into 1st equation:  2.3*B + 3.8*(1 - B) = 2.9

Solve for B:   2.3*B + 3.8 - 3.8*B = 2.9

                    - 1.5*B = -0.9

                      B = 0.6 (which is 60%)  and L = 0.4 (which is 40%)

 

Check work but plugging numbers into first equation:  2.30*0.6 + 3.80*0.4 = 2.90

 

Now, solve for b, the amount of beef in 8 pounds of mixture:

b = 0.6*8 pounds = 4.8 pounds