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?

To put this word problem into a system of equations, we need to define variables for each ingredient and set up equations based on the given information.

Let's denote the number of ounces of dried apples, raisins, and peanuts as follows:

Let "a" be the number of ounces of dried apples.
Let "r" be the number of ounces of raisins.
Let "p" be the number of ounces of peanuts.

We know that one pound is equal to 16 ounces, so we have a total of 16 ounces of trail mix.

Based on the given information, we can set up the following equations:

1) The total cost of the mix is $3.18 per pound:
4.48a + 2.40r + 3.44p = 3.18 * 16

2) The weight of peanuts is twice the weight of dried apples:
p = 2a

3) The total weight of the trail mix is 16 ounces:
a + r + p = 16

These three equations represent the given information in equation form. Now you can solve the system of equations to find the number of ounces of each ingredient.

To put this word problem into a system of equations, we need to assign variables to the unknowns and set up equations based on the given information.

Let's use the following variables:
- Let x represent the weight of dried apples (in ounces) in 1 pound of trail mix.
- Let y represent the weight of raisins (in ounces) in 1 pound of trail mix.
- Let z represent the weight of peanuts (in ounces) in 1 pound of trail mix.

Based on the given information, we can set up three equations:

Equation 1: The total weight of the mixture is 1 pound.
x + y + z = 16 (since there are 16 ounces in 1 pound)

Equation 2: The cost of 1 pound of trail mix is $3.18.
4.48x + 2.40y + 3.44z = 3.18

Equation 3: The weight of peanuts is twice that of dried apples.
z = 2x

Now we have a system of three equations with three variables. To solve this system, we can use various methods such as substitution or elimination, but let's use substitution to solve it.

First, we'll substitute z in Equation 2 with 2x from Equation 3:
4.48x + 2.40y + 3.44(2x) = 3.18

Now, simplify the equation:
4.48x + 2.40y + 6.88x = 3.18
11.36x + 2.40y = 3.18

Now, we have a system of two equations with two variables:
x + y + z = 16 (Equation 1)
11.36x + 2.40y = 3.18 (derived from Equation 2)

From here, you can solve the system of equations using your preferred method, such as substitution or elimination, to find the values of x, y, and z. Once you have the values, you will know the number of ounces of each ingredient in 1 pound of the trail mix.