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

Answer:

The cost of Jelly Beans = $\frac{5}{4}$

The cost of Trail Mix      = $\frac{9}{4}$

Step-by-step 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:

$3J = 6 - \frac{9}{4}$

$\implies 3J = \frac{24 - 9}{4} = \frac{(3)(8 - 3)}{4} = \frac{5}{4}$

∴                                               J  = 5/4