How would I put this word problem into a system of equations (three equations)? Once its in equation form I can easily solve it...

A natural food store makes its own brand of trail mix out of dried apples, raisins, and peanuts. One pound of the mixture costs $3.18. It contains twice as much peanuts by weight of apples. One pound of dried apples costs $4.48, a pound of raisins $2.40, and a pound of peanuts $3.44. How many ounces of each ingredient are contained in 1 pound of the trail mix?

Let A,R, and P represent the fraction of apples, raisins, and peanuts.

P=2A
4.48A+2.40R+3.44P = 3.18
A+R+P=1

Solve for A, R and P (must each be >0).

I need help

To put the word problem into a system of equations, we can define the following variables:

Let A represent the weight (in ounces) of dried apples in 1 pound of the trail mix.
Let R represent the weight (in ounces) of raisins in 1 pound of the trail mix.
Let P represent the weight (in ounces) of peanuts in 1 pound of the trail mix.

We have the following information:

1) The cost of 1 pound of the mixture is $3.18.
2) The mixture contains twice as much peanuts by weight as apples.
3) The cost of 1 pound of dried apples is $4.48.
4) The cost of 1 pound of raisins is $2.40.
5) The cost of 1 pound of peanuts is $3.44.

To translate this information into equations, we can start with the cost equation:

4.48A + 2.40R + 3.44P = 3.18

Next, based on the information that the mixture contains twice as much peanuts by weight as apples, we can write the equation:

P = 2A

Finally, we have the additional information that the weights of the ingredients must add up to 16 ounces (1 pound):

A + R + P = 16

These three equations form the system that can be used to solve the word problem.

To solve this word problem, you need to set up a system of equations based on the given information. Let's break it down.

Let's assume:
Let A be the weight of dried apples in ounces.
Let R be the weight of raisins in ounces.
Let P be the weight of peanuts in ounces.

1. The first equation represents the cost of one pound of the trail mix, which is given as $3.18:
4.48A + 2.40R + 3.44P = 3.18

2. The second equation states that the mixture contains twice as much peanuts by weight as apples:
P = 2A

3. The third equation represents the total weight of one pound of the trail mix:
A + R + P = 16 (since there are 16 ounces in a pound)

Now that you have the system of equations:

4.48A + 2.40R + 3.44P = 3.18
P = 2A
A + R + P = 16

You can solve this system of equations using various methods such as substitution, elimination, or matrices. Once you find the values of A, R, and P, you will have the weight of each ingredient in ounces in 1 pound of the trail mix.