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Abby filled her goodie bags with 4 cookies and 3 candy bars and spent a total of $10.25 per bag. Marissa filled her goodie bags wih 2 cookies and 7 candy bars and spent a total $14.75 per bag. Each cookie costs the same amount. Each candy bar costs the same amount. Write a system of linear equation that can be used to find the cost of one cookie (x) and one candy bar (y). What was the total cost, in dollars, of each candy bar?

Respuesta :

Let's start by writing a system of linear equations:
c -> cookies 
cb -> candy bars
(You can use any abbreviations to your preference)

Abby:
4 cookies 
3 candy bars
$10.25 per bag
The equation would be:
4c+ 3cb = $10.25

Marissa:
2 cookies
7 candy bars
$14.75 per bag
The equation would be:
2c + 7cb = $14.75

So our linear equation system would be:
4c+ 3cb = $10.25
2c + 7cb = $14.75

I would try to get rid of one variable so I can solve for the other variable. In this case, it is easier to get rid of c since I can multiply the second equations by 2. Then it would subtract the two equations.

(2c + 7cb = $14.75) 2 = 4c + 14 cb = $29.50

      4c + 3cb = $10.25
   -  4c+14 cb = $29.50                    (4c would get canceled.)
---------------------------------
             -11 cb = - $19.25                (Divide by -11 to solve for cb)
             ---------   -------------
              -11           -11
            
             cb = $1.75

Now we know cb (candy bar) cost, we would substitute this value into cb into one of the equations. It doesn't matter which equation you put it in. I will substitute it in the first equations. 

  4c + 3 (1.75) = $10.25
  4c + 5.25 = $10.25                       (Multiply 3 by 1.75)
       -5.25       -5.25                         (Subtract 5.25 on both sides)
             4c = 5                                 (Divide by 4 on both sides to get c)
             ----   ---
              4      4
         
         c= 1.25

Check the work:
4(1.25) + 3(1.75) 
  = $10.25

2(1.25) + 7(1.75)
   = $14.75

Total cost:
cookies = $1.25
candy bars = $ 1.75

Hope this helps! :)