SOLUTION: Please help me solve this mixture problem: How many pounds of gourmet candy selling for $2.80 per pound should be mixed with 7 pounds of gourmet candy selling for $1.60 per pou

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Question 552163: Please help me solve this mixture problem:
How many pounds of gourmet candy selling for $2.80 per pound should be mixed with 7 pounds of gourmet candy selling for $1.60 per pound to obtain a mixture selling for $1.96 per pound?
A. 4 lb
B. 3 lb
C. 1 lb
D. 5 lb
I can solve it by trial and error, but is their a formula that will work?
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
How many pounds of gourmet candy selling for $2.80 per pound should be mixed with 7 pounds of gourmet candy selling for $1.60 per pound to obtain a mixture selling for $1.96 per pound?
 +  = 
     ↓      ↓       ↓      ↓       ↓ 
     ↓      ↓       ↓      ↓       ↓
  $2.80x    +    $11.20    =   $1.96(x+7)

Drop the dollar marks and move the decimals two places right

               280x + 1120 = 196(x+7)

               280x + 1120 = 196x + 1372

Subtract 1120 from both sides:

                      280x = 196x + 252

Subtract 196x from both sides:

                       84x = 252

Divide both sides by 84

                      %2884x%29%2F84 = 252%2F84
                          
                        x = 3

Answer 3 pounds.

Edwin