Question

A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.25. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.75. How much does one ounce of peanuts and one ounce of cashews cost?

Answer 1

Given that a store is selling two mixtures of nuts in 20-ounce bags: peanuts and cashews.

Let the cost of one ounce of peanut be x and the cost of one ounce of cashew be y, then

Given that the first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.25 implies that 15x + 5y = 4.25

Also, given that the second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.75 mplies that 5x + 15y = 6.75

To obtain the cost of one ounce of peanuts and one ounce of cashews, we solve the two equations above, simultaneously:
$15x + 5y = 4.25 - - - (1) \\ 5x + 15y = 6.75 - - - (2) \\ \\ (1)\times3\Rightarrow45x+15y=12.75 - - - (3) \\ \\ (2)-(3)\Rightarrow-40x=-6 \\ \\ \bold{x= \frac{-6}{-40} =0.15} \\ \\ From\ (1):15(0.15)+5y=4.25 \\ \\ 5y=4.25-2.25=2 \\ \\ \bold{y= \frac{2}{5} =0.4}$

Therefore, one ounce of peanuts and one ounce of cashews cost $0.15 and $0.40 respectively.