SOLUTION: A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is $24. For 3 pounds of jelly beans and 5 pounds of tra

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Question 1140371: A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mix, the total cost is $24. For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $21. Find the cost of each pound of jelly beans and each pound of trail mix.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
b jelly beans
m trail mix

whatever method you like
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
From the condition, you have these two equations


    6x + 2y = 24      (1)

    3x + 5y = 21      (2)


where x is the price for 1 pound of jelly beans and y is the price for 1 pound of trail mix.


In equation (1), divide both sides by 2.  Keep equation (2) as is.


    3x +  y = 12      (1')

    3x + 5y = 21      (2')


Now subtract equation (1') from equation (2'). You will get


         5y - y = 21 - 9

         4y     =  12

          y     =  12/4 = 3.


So, 3 dollars is the price for 1 pound of trail mix.


To find x, substitute y= 2 into equation (2). You will get


    3x + 5*3 = 21,   or   3x = 21 - 15 = 6  ====>  y = 6/3 = 2.


ANSWER.  $2 for one pound of jelly beans  and  $3 for one pound of trail mix.

Solved.

On the way, I applied the Elimination method to solve the system of 2 equations in 2 unknowns,
so now you know how it works.


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