SOLUTION: A store is having a sale on trail mix and jelly beans. For 2 pounds of trail mix and 3 pounds of jelly beans, the total cost is 14 $. For 6 pounds of trail mix and 5 pounds of

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Question 1206282: A store is having a sale on trail mix and jelly beans. For 2 pounds of trail mix and 3 pounds of jelly beans, the total cost is 14 $. For 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is 28$ . Find the cost for each pound of trail mix and each pound of jelly beans.

Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = cost of 1 pound of trail mix
y = cost of 1 pound of jelly beans

The given sentences translate to the following system
2x+3y = 14
6x+5y = 28

Let's triple both sides of the 1st equation
2x+3y = 14
3*(2x+3y) = 3*14
6x+9y = 42

The original system updates to this
6x+9y = 42
6x+5y = 28

Subtract straight down.
The x terms cancel out.
The y terms subtract to 4y.
The right hand sides subtract to 14

Solving 4y = 14 leads to y = 3.50
Then use that value of y to find x.
2x+3y = 14
2x+3*3.5 = 14
2x+10.5 = 14
2x = 14-10.5
2x = 3.5
x = 3.5/2
x = 1.75

Answers:
Cost of one pound of trail mix = $1.75
Cost of one pound of jelly beans = $3.50
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!

FOOD              PRICE       QTY     COST          QTY       COST

TRAIL MIX           t    |     2       2t     |       6        6t

JELLY BEANS         j    |     3       3j     |       5        5j

COSTS TOTAL                           14                      28



Elimination may be simplest, and to multiply first equation by 3:


Subtract....


-------Jelly Beans, $3.5 per pound.





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