Question

20 pts and a mark!!! 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 $ 12 . For 3 pounds of jelly beans and 5 pounds of trail mix, the total cost is $ 15 . Find the cost for each pound of jelly beans and each pound of trail mix.

Answer 1

The cost of Jelly Beans =
`$ (5)/(4) $`

The cost of Trail Mix =
`$ (9)/(4) $`

Explanation:

Given the cost of 6 pounds of Jelly Beans and 2 pounds of trail mix is $12.

Also, the cost of 3 pounds of Jelly Beans and 5 pounds of Trail mix is $15.

Call the cost of one pound of Jelly beans as J

And cost of one pound of Trail Mix as T.

Now, converting the given data to mathematical form, we would have:

`$ 6J + 2T = 12  $`

Dividing through out by 2 we have:

`$ 3J + T = 6 \hspace{15mm}  .....(1) $`

`$ 3J + 5T = 15 \hspace{15mm} ....(2) $`

To solve (1) and (2), subtract the two equations which will give us:

`$ -4T = - 9 $`

⇒ T = 9/4

Substituting the value of T in (1), we have:

`$ 3J = 6 - (9)/(4) $`

`$ \implies 3J = (24 - 9)/(4) = ((3)(8 - 3))/(4) = (5)/(4) $`

∴ J = 5/4