A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45. Find the cost for each pound of trail mix and each pound of jelly beans.

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

According to the question

A store is having a sale on trail mix and jelly beans .

Let trail mix = T

and jelly beans = J

For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $18.

i.e

5T + 3J = 18 -------------------------- (1)

For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $45.

i.e

2T + 12J = 45 -------------------------------(2)

Now,

multiplying eq (1) from 4

20T + 12J = 72 -----------------(3)

Solving equation (3) and (2) the equation by elimination method

20T + 12J = 72 -----------------(3)

2T + 12J = 45 -------------------------(2)

subtracting equation (2) from (3)

18T = 27

T = 1.5

substituting the value of T in equation 1

5T + 3J = 18

5*1.5 + 3J = 18

7.5 + 3J = 18

3J = 18 - 7.5

3J = 10.5

J = 3.5

Hence, the cost for each pound of trail mix is $1.5 and each pound of jelly beans is $3.5 .

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