a store is having a sale on trail mix and jelly beans. for 2 pounds of trail mix and 3 pound of jelly beans, the total cost is $16. for 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is $34. find the cost for each pound of trail mix and each pound of jelly beans.

Given a store is having a sale on trail mix and jelly beans. For 2 pounds of trail mix and 3 pound of jelly beans, the total cost is $16. For 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is $34. We have to find the cost for each pound of trail mix and each pound of jelly beans.

Let the cost of each pound of trail mix is $x.

and the cost of each pound of jelly beans is $y.

According to question,

For 2 pounds of trail mix and 3 pound of jelly beans, the total cost is $16.

⇒ 2x+3y=16 → (1)

For 6 pounds of trail mix and 5 pounds of jelly beans, the total cost is $34.

⇒ 6x+5y=34 → (2)

Solving (1) and (2), we get

3(1 equation)-(2 equation)=0

⇒ 3(2x+3y-16)-(6x+5y-34)=0

⇒ 4y=14 ⇒ y=3.5

hence,

2x+3(3.5)=16 ⇒ x=2.75

Hence, the cost for each pound of trail mix and each pound of jelly beans is $2.75 and $3.5 respectively.

JeanaShupp JeanaShupp · Answer 2 · 2019-02-25T10:19:07+01:00

Answer: The cost of each pound of trial mix = $2.75

The cost of each pound of jelly beans = $3.5

Step-by-step explanation:

Let the cost of each pound of trail mix be x and the cost of each pound of jelly bean be y.

Then according to the question, we have the following system,

[tex]2x+3y=16.....(1)\\6x+5y=34........(2)[/tex]

Multiply 3 on both the sides of equation (1), we get

[tex]6x+9y=48.................(3)[/tex]

Eliminate equation (2) from (3), we get

[tex]4y=14\\\Rightarrow\ y=\frac{7}{2}=3.5[/tex]

Substitute the value of y in equation (1), we get

[tex]2x+3(3.5)=16\\\Rightarrow\ 2x=16-10.5\\\Rightarrow\ 2x=5.5\\\Rightarrow\ x=\frac{5.5}{2}=2.75[/tex]

Hence, the cost of each pound of trial mix = $2.75

The cost of each pound of jelly beans = $3.5